Question

How do you use substitution to solve the system of equations `2x+y=-7` and `-5x+2y = 22`?

Answer 1

`x = -4, y =1`

Explanation:

The clue that substitution would be a good method, is the
single `y` term in the first equation.

`2x +color(red) y = -7" "rArr color(red)(y = -2x-7)`

In the other equations, replace `color(red)(y)` by `color(red)((-2x-7))`

`-5x +2color(red)y = 22`

`-5x +2color(red)((-2x-7)) = 22`

`-5x -4x-14 = 22`

`-9x = 22+14`

`-9x = 36" "color(blue)(x = -4)`

Now that we know the value for `x`, sub it to find y.

`y = -2color(blue)((-4))-7`

`y = +8-7 = 1" "color(red)(y=1)`