Question

How do you solve this system of equations: `-5x - 7y = - 15 and 5x + 9y = 5`?

Answer 1

`x=10`
`y=-5`

Explanation:

Add the two equations together first:

`->` `-5x -7y = -15`
`(+)` `5x` `+9y = 5`

Adding both left sides of each equals sign together, the x values cancel out ( `-5x + 5x = 0`) , and `-7y + 9y = 2y`

Adding both right sides of the two equations `-15 + 5 = -10`

That leaves us with `2y=-10`
then divide both sides by 2 to get:
`y = -5`

You can then fill that into either of the original equations to find x

`5x + 9y=5`
`5x+9(-5)=5`
`5x -45 = 5`
Add 45 to both sides
`5x = 50`
divide both sides by 5
`x = 10`

It's also recommended to check your answer in the other equation:

`x=10`
`y=-5`

`-5x -7y = -15`
`-5(10) -7(-5)= -15`
`-50 +35 = -15`
`-15 = -15`

Correct! :)