Question

How do you solve `-2x+3y=15` and `-6x+6y=18` using substitution?

Answer 1

See a solution process below:

Explanation:

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

`-6x + 6y = 18`

`(-6x + 6y)/color(red)(6) = 18/color(red)(6)`

`(-6x)/color(red)(6) + (6y)/color(red)(6) = 3`

`-x + y = 3`

`-x + color(red)(x) + y = 3 + color(red)(x)`

`0 + y = 3 + x`

`y = 3 + x`

Step 2) Substitute `(3 + x)` for `y` in the first equation and solve for `x`:

`-2x + 3y = 15` becomes:

`-2x + 3(3 + x) = 15`

`-2x + (3 xx 3) + (3 xx x) = 15`

`-2x + 9 + 3x = 15`

`-2x + 9 - color(red)(9) + 3x = 15 - color(red)(9)`

`-2x + 0 + 3x = 6`

`-2x + 3x = 6`

`(-2 + 3)x = 6`

`1x = 6`

`x = 6`

Step 3) Substitute `6` for `x` in the solution to the second equation at the end of Step 1 and calculate `y`:

`y = 3 + x` becomes:

`y = 3 + 6`

`y = 9`

The Solution Is:

`x = 6` and `y = 9`

Or

`(6, 9)`