Question

How do you solve the system `x+6y=-22` and `-6x-2y=-4` by substitution?

Answer 1

The solution for the system of equations is
`color(red)(x = 2 , y=-4`

Explanation:

`x+6y=-22`
`x=color(red)(-22 - 6y` ..................equation `(1)`
`-6x-2y=-4` ............equation `(2)`

Substituting equation `(1)` in equation `(2)` to find `y`

`-6x-2y=-4`
`-6color(red)((-22 -6y))-2y=-4`
`132 +36y -2y =-4`
`132 +34y=-4`
`34y=-136`
`color(red)(y=-4`

Substituting `y` in equation `1` to find `x`
`x = -22 - 6y`
`x = -22 -6.(-4)`
`x = -22+24`
`color(red)(x = 2`