Angela belongs to a baking
club. She pays a one-time
membership fee and then.
receives baking recipes and
supplies at a discounted rate.
After receiving 4 recipes,
Angela had spent $85. After
receiving 10 recipes, she had
spent $160. Write an equation
to represent this situation.

Please help.

$1800 is the amount invested

An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed. The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, deposited, or borrowed.

Nico invests some money at 8%;

let M = amount invested

Nico also invests M - 800 at 7%

After 1 year, the total interest is $214.

M (0.08) + (M - 800)0.07 = $214

0.08M + 0.07M - 56 = $214

0.15M - 56 =  $214

0.15M = $160 + $56

0.15M = $270

Divide both sides of the equation by 0.15

M = $1800

Hence, the amount invested is $1800

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Answer:

26

Step-by-step explanation:

2 squared equals 4. So 30 - 4 = 26

hope it helps!

Using the general formula for the mean, we can see that the mean between 0.6149 and 0.6236 is 0.61925

Suppose we have any set of N numbers:

{x₁, x₂, ..., xₙ}

The mean of these values is given by:

mean = (x₁ + x₂ + ... + xₙ)/N

In this case we want to find the mean between two numbers,  0.6149 to 0.6236

This will be:

mean = (0.6149 + 0.6236)/2 = 0.61925

We can see that the mean between  0.6149 and 0.6236 is 0.61925

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Answer:

The answer is 1720ㅤㅤㅤㅤㅤㅤㅤㅤ

Answer:

Step-by-step explanation:

To calculate Jason's profit, we can subtract his total expenses from his total revenue.

First, let's calculate the cost of the T-shirts:

200 T-shirts * R10 each = R2000

Next, let's calculate the cost of screen printing:

200 T-shirts * R1 to screen print each = R200

Now, let's calculate the total cost:

R2000 + R200 = R2200

Next, let's calculate Jason's total revenue:

200 T-shirts * R35 each = R7000

Finally, let's subtract the total cost from the total revenue to find the profit:

R7000 - R2200 = R4800

So Jason made a profit of R4800 by selling 200 T-shirts.

Note: It seems there is a typo in the question as it mentions "which she calls at 850 each", which doesn't seem to be related to the calculation of Jason's profit.

The height of the right cone will be 57 units.

The area a cone takes up in a three-dimensional plane is known as its volume. A cone's base is circular, so it is made of a radius and a diameter.

Given that the volume of a right cone is 4275π cubic units. The circumference of the cone is 30π.

The height of the cone will be calculated as below:-

First, calculate the radius of the base of the cone,

Circumference = 2πr

30π = 2πr

r = 15 units

The height of the cone:-

Volume = 4275π

( 1 / 3 ) πr²h =  4275π

h = ( 4275 x 3 ) / r²

h = ( 4275 x 3 ) / ( 15)²

h = 57 units

Hence, the height will be 57 units.

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Answer:

Step-by-step explanation:

To find the x-coordinates of the points where the curve with the equation y = x³ - 4x² + 5x + 4 has a gradient of 1, we need to find the points where the derivative of the equation y = x³ - 4x² + 5x + 4 is equal to 1. The derivative of the equation y = x³ - 4x² + 5x + 4 is given by:

dy/dx = 3x² - 8x + 5

So, we need to find the solutions of the equation:

3x² - 8x + 5 = 1

This is a quadratic equation that can be solved by factoring, completing the square, or using the quadratic formula. To use the quadratic formula, we can write:

x = (-b ± √(b² - 4ac)) / (2a)

Where a = 3, b = -8, and c = 4. Plugging in these values, we get:

x = (-(-8) ± √((-8)² - 4 * 3 * 4)) / (2 * 3)

x = (8 ± √(64 - 36)) / 6

x = (8 ± √(28)) / 6

x = (8 ± 2√7) / 6

So, the two solutions are:

x = (8 + 2√7) / 6 and x = (8 - 2√7) / 6

These are the x-coordinates of the points where the curve with the equation y = x³ - 4x² + 5x + 4 has a gradient of 1.

The missing value in the expression is 6x²

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is an expression, (-4x²+ 6x + 3) + (8x + 5+ ?) = 2x² + 14x + 8 we need to find the missing value in the expression,

(-4x²+ 6x + 3) + (8x + 5+ ?) = 2x² + 14x + 8

-4x²+ 6x + 3 + 8x + 5+ ? = 2x² + 14x + 8

-4x²+14x+8+? = 2x² + 14x + 8

14x-14x+8x-8x+? = 2x² + 4x²

? = 6x²

Hence, the missing value in the expression is 6x²

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The total amount spent by Ivan is given by the equation A = $ 40.20

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount spent by Ivan be represented as A

Now , the equation will be

The cost of one large necklace = $ 5.90

The cost of one small necklace = $ 4.90

The number of large necklaces = 1

The number of small necklaces = 7

So , the cost of 7 small necklaces = 7 x cost of one small necklace

Substituting the values in the equation , we get

The cost of 7 small necklaces = 7 x $ 4.90

The cost of 7 small necklaces = $ 34.30

And , the total amount spent by Ivan = cost of one large necklace + cost of 7 small necklaces

On simplifying the equation , we get

The total amount spent by Ivan A = 5.90 + 34.30

The total amount spent by Ivan A = $ 40.20

Hence , the equation is A = $ 40.20

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The expression for the perimeter of the frame is 128 inches + 10w.

Width of the mat = 4w

width of the frame = w

Now,

Let the length of the poster be = L

Let the width of the poster = W.

Therefore,  According to the question,

L = 48 inches and W = 16 inches.

The total width of the mat and frame around the poster will be -

= 4w + w

= 5w.

Calculating the perimeter of the frame -

= 2 (L + W + 5w),

= 2 (48 + 16  + 5w)

= 2 (64 + 5w)

= 128 + 10w.

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Answer:

The two alarm clocks will ring together again at 2:54 p.m

Answer:

y=4(x−2) ^2−14

Step-by-step explanation:

The equation for the sphere is [tex](x-5)^2 + (y-1)^2 + (z-4)^2 = r^2[/tex] , that passes through the point (5, 1, 4) and is tangent to all three coordinate planes.

A sphere centered at the point (x0, y0, z0) with a radius of r can be represented by the equation [tex](x-x0)^2 + (y-y0)^2 + (z-z0)^2 = r^2.[/tex]

Therefore, a sphere that passes through the point (5, 1, 4) and is tangent to all three coordinate planes can be represented by substituting the values of x0, y0, and z0: [tex](x-5)^2 + (y-1)^2 + (z-4)^2 = r^2[/tex], where r is the radius of the sphere and is equal to the distance from the center of the sphere to the tangent point on the coordinate plane.

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The amount after 15 years with interest compounded quarterly is given by the equation A = $ 4,231.79

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

Let the amount after 15 years be represented as A

Now , the equation will be

Let the principal amount be P = $ 3000

Let the number of years be b = 15 years

Let the number of times interest is applied be n = 4

Let the percentage of interest be r = 2.3 %

And , A = P ( 1 + r/n )ⁿᵇ

Substituting the values in the equation , we get

A = 3000 ( 1 + 0.023/4 )⁴ˣ¹⁵

A = 3000 ( 1 + 0.00575 )⁶⁰

On further simplification , we get

A = 3000 ( 1.00575 )⁶⁰

A = $ 4,231.79

Therefore , the compound interest is I = $ 1,231.49

Hence , the amount after 15 years is $ 4,231.79

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The differential equation (y^2 cos(x−y) −x^2 sin(x−y)) dx+(2xycos(x−y) +x^2 sin(x−y)) dy =0 is not exact, because it cannot be written in the form F(x,y)dx + G(x,y)dy = 0 for some functions F and G.

b. The differential equation (2x+12y^2)dx+(12x+2y)dy=0 is exact, because it can be written in the form F(x,y)dx + G(x,y)dy = 0 for F(x,y) = 2x + 12y^2 and G(x,y) = 12x + 2y.

To find a general solution in an implicit form, we can integrate both sides:

∫ (2x + 12y^2) dx + ∫ (12x + 2y)dy = C

x^2 + 6y^2 + 12xy = C

c. The differential equation (12x^2 + 2y) dx+(2x + 12y^2)dy=0 is not exact, because it cannot be written in the form F(x,y)dx + G(x,y)dy = 0 for some functions F and G.

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As two distinct ordered pairs (6, 5) and (6, 10) have the same first coordinate the relation is not a function.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

We know a relation is a function if it is one-to-one and many-to-one.

And, A relation is not a function if it is one to many.

From the given arrow diagram.

The domain of the relation is, {3, 6, 12, 18} and the range of the relation is

{5, 7, 9, 10}.

But preimage 6 has two different images namely 5 and 10 so the relation is not a function.

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30. The pair of angles equal in measurement are ∠1 and ∠9.

31. The sum of the angles x and y is 165 degrees.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, vertically opposite angles etc.

Therefore, let's use the angle relationships to find the missing angles in the parallel lines.

Therefore, ∠1 and ∠9 are corresponding angles. Hence, they are congruent.

Let's find the angles x and y to know the sum of the angles.

Therefore,

x = 55 degrees(corresponding angles)

y = 180 - 70 = 110(sum of angles on a straight line)

Therefore,

x + y  = 55 + 110 = 165 degrees.

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The Central Limit Theorem states that if the population is normally distributed and the sample size is reasonably large, then the sample mean will be normally distributed.

The Central Limit Theorem states that if the sample size is reasonably large and the population is normally distributed, then the sample mean will be normally distributed. This means that we can use the normal distribution to make inferences about the population mean. Specifically, it allows us to calculate the probability that the population mean falls within a certain range, given the sample mean. This is useful because we can use the sample data to make assumptions about the population as a whole. For example, if the sample data is normally distributed, we can assume that the population mean is also normally distributed. This is especially useful when the population size is large and it would be difficult to collect data from every individual in the population. The Central Limit Theorem gives us an efficient way to make inferences about the population mean.

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Solve the equation y = f(x) to determine the values of the independent variable x and obtain the domain.

What is meant by domain and range?

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Solve the equation y = f(x) to determine the values of the independent variable x and obtain the domain.

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

All of the values that can go into a relation or function (input) are called the domain. All of the values that come out of a relation or function (output) are called the range.

To find the domain and range, we simply solve the equation y = f(x) to determine the values of the independent variable x and obtain the domain. To calculate the range of the function, we simply express x as x=g(y) and then find the domain of g(y).

Given equation: y=f(x)

We can solve for the value of x by rearranging the equation to the form x = [tex]f^{-1y}[/tex]

Domain:

x = [tex]f^{-1y}[/tex]

The domain of f(x) is all the possible values of x for which y is defined.

Range:

y = g(x)

The range of g(x) is all the possible values of y for which x is defined.

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Elementary row operations to find system of equation solutions in row echelon or reduced row echelon form.

We first write the augmented matrix [A|B] by combining the coefficients of the variables and the constants on the right side of the equations:

x + y + 6z | 8

1/3 x - 1/3 y + 2/3 z | 2

1/2 x | -z | 0.

Here are the steps to perform Gauss-Jordan row reduction on the augmented matrix [A|B]:

Step 1: Divide the first row by x + y + 6z to get 1 as the leading coefficient:

1 y/x + y + 6z 6z/x + y + 6z | 8/x + y + 6z

1/3 x - 1/3 y + 2/3 z | 2

1/2 x | -z | 0

Step 2: Subtract the first row multiplied by 1/3 from the second row to eliminate x:

1 y/x + y + 6z 6z/x + y + 6z | 8/x + y + 6z

0 - 2/3 y + 5/3 z | 4/3

1/2 x | -z | 0

Step 3: Subtract the first row multiplied by 1/2 from the third row to eliminate x:

1 y/x + y + 6z 6z/x + y + 6z | 8/x + y + 6z

0 - 2/3 y + 5/3 z | 4/3

0 | -z + 3z/x + y + 6z | 3/x + y + 6z

Step 4: Divide the second row by -2/3 to get 1 as the leading coefficient:

1 y/x + y + 6z 6z/x + y + 6z | 8/x + y + 6z

0 1 5/2 | -2/3

0 | -z + 3z/x + y + 6z | 3/x + y + 6z

Step 5: Subtract the second row multiplied by 5/2 from the third row to eliminate y:

1 y/x + y + 6z 6z/x + y + 6z | 8/x + y + 6z

0 1 5/2 | -2/3

0 | 3z | -15/2

Step 6: Divide the third row by 3 to get 1 as the leading coefficient:

1 y/x + y + 6z 6z/x + y + 6z | 8/x + y + 6z

0 1 5/2 | -2/3

0 | 1 | -5

Thus, the reduced row echelon.

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The remark in the problem is the statement that the forces can be associated with potential energies is explained as follows: the work from x=3.00m to x=2.00m is

W=F₂ Δx=(5.00N)(−1.00m)=−5.00J,

so the potential energy at x=2.00m is U₂=+5.00J.

(b Now, we should evident from the problem statement that Emax =14.0J, so the kinetic energy at x=2.00m is the kinetic energy at x=2.00m is

K₂=Emax−U₂=14.0−5.00=9.00J.

(c) the work from x=2.00m to x=0 is W=F₁Δx=(3.00N)(−2.00m)=−6.00J, so the potential energy at x=0 is

U₀=6.00J+U₂=(6.00+5.00)J=11.0J.

(d) Similar to reasoning presented in part (a) then gives

K₀=Emax−U₀=(14.0−11.0)J=3.00J.

(e) The work from x=8.00m to x=11.0m is

W=F₃Δx=(−4.00N)(3.00m)=−12.0J,

so the potential energy at x=11.0m is U₁₁=12.0J.

(f) The kinetic energy at x=11.0m is therefore

K₁₁=Emax−U₁₁=(14.0−12.0)J=2.00J.

(g) Now we have W=F₄Δx=(−1.00N)(1.00m)=−1.00J, so the potential energy at x=12.0m is

U₁₂=1.00J+U₁₁=(1.00+12.0)J=13.0J.

(h) Thus, the kinetic energy at x=12.0m is

K₁₂=Emax−U₁₂=(14.0−13.0)=1.00J.

(i) T There is no work done in the interval of x=12.0m to x=13.0m so the answers are the same as in part (g): U₁₂=13.0J.

.(j) In this also there is no work done in this interval so the answers are the same as in part (h): K₁₂=1.00J.

(k)  Although the plot is not shown here, it would look like a “potential well” with piecewise-sloping sides: from x=0 to x=2 the graph of U is decreased from the line segment with 11 to 5, and from x=2 to x=3

it may be headed down to zero, where it stays until x=8, where it starts to increase to a value of 12 at which x=11, and in another positive-slope line segment it increased to the value of 13 at x=12.

For x>12 it is a value that does not change.

(l) The particle can be thought of as “falling” down the 0<x<3  slopes of the well, gaining kinetic energy as it does so, and certainly is able to reach x=5. Since U=0 at x=5, then its initial potential energy (11J) has completely converted to kinetic: now K=11.0J.

(m) This is not sufficient to climb up and out of the well on the large x side (x>8), but does allow it to reach a “height” of 11 at x=10.8m. As discussed in sections 8−5, this is a “turning point” of the motion.

(n) Next it “falls” back down and rises back up the small x slope until it comes back to its original position. Stating this more carefully, when it is stopped at x=10.8m it is accelerated to the left by the force  F₃.

it gains enough speed as a result that it eventually is able to return to x=0, where it stops again.

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Step-by-step explanation:

Factor the denominator to simplify the expression: x^2 + x - 2 = (x - 1)(x + 2)

Use partial fraction decomposition to write the integrand as the sum of simpler terms: (x^3 + 2x^2 + 3x + 4)/(x^2 + x - 2) = A/(x - 1) + B/(x + 2) + Cx + D, where A, B, C, and D are constants.

Multiply both sides of the equation by (x^2 + x - 2) to find the values of A, B, C, and D: x^3 + 2x^2 + 3x + 4 = A(x + 2) + B(x - 1) + (Cx + D)(x^2 + x - 2)

Substitute x = 1 and x = -2 into the equation to find two equations for A, B, C, and D:

x = 1: 4 + 2 + 3 + 4 = 9 = A(-2) + B + (C + D)(-1)

x = -2: -8 - 4 + 6 - 8 = -16 = A(1) + B(-2) + (C - 2D)(4)

Solve the system of equations to find the values of A, B, C, and D:

A = 9/3, B = 5, C = -11/3, D = 7/3

Use the partial fraction decomposition to integrate the integrand:

Integral of 1/(x - 1) = ln|x - 1|

Integral of 1/(x + 2) = ln|x + 2|

Integral of x = x^2/2

Integral of 1 = x

Evaluate the definite integral by subtracting the values of the antiderivatives at the limits of integration:

Integral from x=0 to x=1 of (x^3 + 2x^2 + 3x + 4)/(x^2 + x - 2) = (ln|x + 2| - ln|x - 1| + x^2/2 - x)|x=1 - x=0 = (ln(3) - ln(-1) + 1/2 - 1) = (ln(3) + ln(1) + 1/2) = ln(3) + 1.

So the definite integral of (x^3 + 2x^2 + 3x + 4)/(x^2 + x - 2) from x=0 to x=1 is equal to ln(3) + 1.

Answer:

Step-by-step explanation:

The maximum possible cost of a portion of fish is £4.

The cost of a product or service is the amount of money spent on it. It is the whole cost of purchasing, manufacturing, or producing something. The cost of a work may also refer to the amount of time and effort required to finish it. When determining whether or not to buy a product or service, cost is a crucial consideration, and it may be influenced by a number of variables such as material prices, labor expenses, overhead, and demand.

A piece of fish can cost no more than £4.

We may use the following equation to figure this out:

5 servings of fish at £f each + 2 bags of chips at £2 each = £20

This equation may then be rearranged to solve for f:

f = (20 - (2 x 2))/5

f = 16/5

f = £3.20

As a result, the most a slice of fish may cost is £4.

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Answer:

The single transformation that takes shape P to shape Q is a dilation by a scale factor of 3 with a center of dilation at (1, 0)

Step-by-step explanation:

In general, if the range of a function is y≥−1, its inverse has a domain of y≥−1. So, the range of the inverse of the cubic root function is y≥−1.

The range of a cubic root function becomes the domain of a cube function and vice versa since a cubic root function is an inverse function of a cube function. Therefore, the cube function's range is x3 if the cubic root function's domain is x3.

A function's inverse typically has a domain of y1 if its range is y1. Therefore, y1 is the domain of the inverse of the cubic root function.

Describe a function.

A function is a mathematical relationship between a domain—a set of inputs—and a range—a set of outputs. Each input in the domain is given a distinct output, known as the function value, by a function. An equation or graph can be used to depict the function value.

A function is typically represented symbolically by an equation that describes the relationship between the inputs and outputs and a letter, like f or g, as well as the letter. For instance, the equation of a function that accepts a value of x as input and produces its square is f(x) = x2.

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The professor sorted her students according to their majors which in this case acted as labels so the Professor was using the Nominal measurement scale

When the Nominal measurement scale is used, it means the data was sorted into labels or names which is why it is sometimes referred to as Named data. For instance, sorting dogs in a park into their species i.e Husky, American Bull, German Shephard, etc.  

There is no quantitative value and usually, there is no ordering method for this measurement scale.

The professor sorted her students according to their majors which in this case acted as labels so the Professor was using the Nominal measurement scale

.

b)

     Major                           Number of students

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The exponential expression in the format cx^n is given as follows:

2.5x^(-6).

The expression for this problem is defined as follows:

5/(2x^6).

The desired format is given as follows:

cx^n.

For the parameter c, we must simply divide the numeric coefficients of the numerator and the denominator, hence:

5/2 = 2.5.

For the parameter n, we have the positive exponent in the denominator, hence it can be written as a negative exponent in the numerator, that is:

n = -6.

Hence the expression is given as follows:

2.5n^(-6).

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The impact of the virus on the forest is a decrease of 73 trees per month, or a decrease of 73% each month.

The formula for predicting the number of trees after m months since the virus's discovery is T=x(0.73)m, where T represents the number of trees, x represents the original number of trees that existed in the forest when the scientists made the discovery, and m represents the number of months since the virus's discovery.

For example, if the original number of trees in the forest was 100 and the virus was discovered 3 months ago, then the model predicts that the number of trees in the forest after 3 months since the virus's discovery is T = 100(0.73)3 = 51.7. This means that the number of trees in the forest decreased by 48.3 (100-51.7) over the 3 months since the virus's discovery, which is equivalent to a decrease of 48.3/100 = 0.483 = 48.3%. This also means that the number of trees in the forest is decreasing by 48.3% = 0.483 each month, which is equivalent to a decrease of 73 trees per month (100 x 0.483).

Therefore, the impact of the virus on the forest is a decrease of 73 trees per month, or a decrease of 73% each month.

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Answer:

x=3

Y=−4

Step-by-step explanation:

Y=−7/3x+3

Y=−1/3x−3

​

Consider the first equation. Add  

3

7

​

x to both sides.

Y+

3

7

​

x=3

Consider the second equation. Add  

3

1

​

x to both sides.

Y+

3

1

​

x=−3

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

Y+

3

7

​

x=3,Y+

3

1

​

x=−3

Choose one of the equations and solve it for Y by isolating Y on the left hand side of the equal sign.

Y+

3

7

​

x=3

Subtract  

3

7x

​

 from both sides of the equation.

Y=−

3

7

​

x+3

Substitute −

3

7x

​

+3 for Y in the other equation, Y+

3

1

​

x=−3.

−

3

7

​

x+3+

3

1

​

x=−3

Add −

3

7x

​

 to  

3

x

​

.

−2x+3=−3

Subtract 3 from both sides of the equation.

−2x=−6

Divide both sides by −2.

x=3

Substitute 3 for x in Y=−

3

7

​

x+3. Because the resulting equation contains only one variable, you can solve for Y directly.

Y=−

3

7

​

×3+3

Multiply −

3

7

​

 times 3.

Y=−7+3

Add 3 to −7.

Y=−4

The system is now solved.

Y=−4,x=3