Question

How do you solve the following with substitution?

`4x - y = (-24)`
`6x + 3y = (-9)`

Answer 1

See a solution process below:

Explanation:

Step 1) Solve the first equation for `y`:

`4x - y = -24`

`4x - y + color(blue)(y) + color(red)(24) = -24 + color(red)(24) + color(blue)(y)`

`4x - 0 + 24 = 0 + y`

`4x + 24 = y`

`y = 4x + 24`

Step 2) Substitute `(4x + 24)` for `y` in the second equation and solve for `x`:

`6x + 3y = -9` becomes:

`6x + 3(4x + 24) = -9`

`6x + (3 xx 4x) + (3 xx 24) = -9`

`6x + 12x + 72 = -9`

`(6 + 12)x + 72 = -9`

`18x + 72 = -9`

`18x + 72 - color(red)(72) = -9 - color(red)(72)`

`18x + 0 = -81`

`18x = -81`

`(18x)/color(red)(18) = -81/color(red)(18)`

`(color(red)(cancel(color(black)(18)))x)/cancel(color(red)(18)) = -(9 xx 9)/color(red)(9 xx 2)`

`x = -9/2`

Step 3) Substitute `-9/2` for `x` in the solution to the first equation at the end of Step 1 and calculate `y`:

`y = 4x + 24` becomes:

`y = (4 xx -9/2) + 24`

`y = -36/2 + 24`

`y = -18 + 24`

`y = 6`

The Solution Is: `x = -9/2` and `y = 6` or `(-9/2, 6)`