Question

How do I solve substitution with picture ??

Answer 1

a) No Solutions

Explanation:

It might be helpful to first get the equations in terms of y = mx + b.

The first equation (4x + 4y = -8) can be rewritten like this:

4x + 4y = -8 (original equation)

4y = 4x - 8 (subtract 4x from both sides)

y = x - 4 (divide everything by 4 to get y on its own)

and now you have an equation in terms of y = mx = b, where m is 1 and b is -4.

The second equation can be written like this:

2x + 2y = -4 (original equation)

2y = 2x - 4 (subtract 2x from both sides)

y = x - 2 (divide everything by 2 to get y on its own)

and once again we have an equation with m being 1 and b being -2.

So hopefully you should see that the equations will never touch because they have the same slope. Because the equations never touch, they have no solutions. Have a look at the graph.

Answer 2

no solution

Explanation:

If you divide the first equation by 2 you get:

2x+2y=4 (first equation after dividing both sides by 2)

2x+2y=-4 (second equation)

This is setup for elimination.

Subtract the equations:

2x+2y=4

2x+2y=-4

--------------Subtracting!

0+0=8

0=8

0=8 is a false equation which implies the system has no solution.