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Solve the system of equations and write each equation in slope-intercept form:

Equation 1: 2x + y = 3
Equation 2: -2y = 14 - 6x

User Ddpishere
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2 Answers

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Answer:

To solve the system of equations and write each equation in slope-intercept form, we can follow these steps:

1. Equation 1: 2x + y = 3

To write this equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we need to isolate y on one side of the equation.

First, subtract 2x from both sides of the equation:

y = -2x + 3

Now the equation is in slope-intercept form.

2. Equation 2: -2y = 14 - 6x

To write this equation in slope-intercept form, we need to isolate y.

First, divide both sides of the equation by -2 to solve for y:

y = (-14 + 6x) / 2

y = -7 + 3x

Now the equation is in slope-intercept form.

To solve the system of equations, we can set the two equations equal to each other and solve for x:

-2x + 3 = -7 + 3x

Add 2x to both sides:

3 = 5x - 7

Add 7 to both sides:

10 = 5x

Divide both sides by 5:

x = 2

Now that we have the value of x, we can substitute it back into either of the original equations to solve for y. Let's use Equation 1:

2(2) + y = 3

4 + y = 3

y = -1

Therefore, the solution to the system of equations is x = 2 and y = -1. The equations in slope-intercept form are:

Equation 1: y = -2x + 3

Equation 2: y = -7 + 3x

Explanation:

User Stoogy
by
8.4k points
3 votes

To solve the system of equations and write each equation in slope-intercept form, we can follow these steps:

1. Equation 1: 2x + y = 3

To write this equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we need to isolate y on one side of the equation.

First, subtract 2x from both sides of the equation:

y = -2x + 3

Now the equation is in slope-intercept form.

2. Equation 2: -2y = 14 - 6x

To write this equation in slope-intercept form, we need to isolate y.

First, divide both sides of the equation by -2 to solve for y:

y = (-14 + 6x) / 2

y = -7 + 3x

Now the equation is in slope-intercept form.

To solve the system of equations, we can set the two equations equal to each other and solve for x:

-2x + 3 = -7 + 3x

Add 2x to both sides:

3 = 5x - 7

Add 7 to both sides:

10 = 5x

Divide both sides by 5:

x = 2

Now that we have the value of x, we can substitute it back into either of the original equations to solve for y. Let's use Equation 1:

2(2) + y = 3

4 + y = 3

y = -1

Therefore, the solution to the system of equations is x = 2 and y = -1. The equations in slope-intercept form are:

Equation 1: y = -2x + 3

Equation 2: y = -7 + 3x

User MGDroid
by
8.7k points

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