Question

What is the solution to the system of equations: `5x + 2y = -7`, and `-5x + y = 19`?

Answer 1

`(-3,4)`

Explanation:

We have:

`((5x+2y=-7),(-5x+y=19))`

Adding the two equations, we get:

`3y=12`

`y=4`

Inputting this into one of the equations:

`5x+2(4)=-7`

`5x=+8=-7`

`5x=-15`

`x=-3`

So the solution set is `(-3,4)`

Answer 2

`color(darkred)(therefore x=-3 and y=4`

Explanation:

`-5x+y=19`

`y=19+5x`

Given that,

`5x+2y=-7`

`5x+2(19+5x)=-7`

`5x+38+10x=-7`

`5x+10x=-7-38`

`15x=-45`

`x=-45/15`

`color(red)(x=-3`

`y=19+5x`

`y=19+5xx-3`

`y=19-15`

`color(magenta)(y=4`

`color(darkred)(therefore x=-3 and y=4`

~Hope this helps! :)