how to solve then graph

Question

3x-2y=-8

2x + y=-3

Answer 1

What are we trying to solve here? Are we looking for the intersection of those two lines? If so, then the first thing we should do is convert it into this format: y = ax + b

1)

3x - 2y = -8 

2y = 3x + 8 

y = 1.5x + 4

 

2)

2x + y = -3

y = -2x - 3

 

Then we set them equal to each other:

3)

-2x - 3 = 1.5x + 4 

-7 = 3.5x

x = -2

y = 1

 

 

Answer 2

In order to graph these equations the best thing to do is get them into the slope intercept form (y = mx + b)

 

First equation:

3x-2y = -8

 

Add 3x to both sides

 

-2y = -3x - 8

 

Divide by -2 on both sides

 

y = 3/2 x + 4 

 

This equation has a y intercept of (0,4) and has a 3/2 slope (up from bottom left to top right, slightly greater than a 45 degree angle).

 

Second equation:

 

2x + y = -3

 

Subtract 2x from both sides

 

y = -2x - 3

 

This equation has a y intercept of (0, -3) and has a -2 slope (down from top left to bottom left, even more steep than a 45 degree angle).

 

To solve the equation, we can either graph the two lines carefully to find the solution or solve the system of equations.

 

To solve the system, multiply the second equation by 2 and add to the first equation:

 

  3x - 2y = -8

+4x +2y = -6

 

7x = -14

 

Divide by 7 on both sides

 

x = -2

 

Substitute back into either equation:

 

3(-2) - 2y = -8

 

-6 - 2y = -8

 

Add 6 to both sides

 

-2y = -2

 

Divide by -2 on both sides

 

y = 1

 

Solution is (-2, 1)

 

Check solution in both equations.

 

3(-2) - 2(1) = -8      -6 - 2 = -8     check

 

2(-2) + 1 = -3         -4 + 1 = -3     check