Question

How do you solve the system of equations`6x + 8= 8y` and `- 2y = x + 8`?

Answer 1

See a solution process below: `(-4, -2)`

Explanation:

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

`-2y = x + 8`

`-2y - color(red)(8) = x + 8 - color(red)(8)`

`-2y - 8 = x + 0`

`-2y - 8 = x`

`x = -2y - 8`

Step 2) Substitute `(-2y - 8)` for `x` in the first equation and solve for `y`:

`6x + 8 = 8y` becomes:

`6(-2y - 8) + 8 = 8y`

`(6 xx -2y) + (6 xx -8) + 8 = 8y`

`-12y + (-48) + 8 = 8y`

`-12y - 48 + 8 = 8y`

`-12y - 40 = 8y`

`-12y + color(red)(12y) - 40 = 8y + color(red)(12y)`

`0 - 40 = (8 + color(red)(12))y`

`-40 = 20y`

`-40/color(red)(20) = (20y)/color(red)(20)`

`-2 = (color(red)(cancel(color(black)(20)))y)/cancel(color(red)(20))`

`-2 = y`

`y = -2`

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

`x = -2y - 8` becomes:

`x = (-2 xx -2) - 8`

`x = 4 - 8`

`x = -4`

The Solution Is:

`x = -4` and `y = -2`

Or

`(-4, -2)`