Question

How do you solve the system of equations `8x - 8y = - 16` and `- 2x + 4y = 14`?

Answer 1

See the entire solution process below:

Explanation:

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

`8x - 8y = -16`

`(8x - 8y)/color(red)(8) = -16/color(red)(8)`

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

`x - y = -2`

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

`x - 0 = y - 2`

`x = y - 2`

Step 2) Substitute `y - 2` for `x` in the second equation and solve for `y`:

`-2x + 4y = 14` becomes:

`-2(y - 2) + 4y = 14`

`(-2 * y) - (-2 * 2) + 4y = 14`

`-2y + 4 + 4y = 14`

`4y - 2y + 4 = 14`

`(4 - 2)y + 4 = 14`

`2y + 4 = 14`

`2y + 4 - color(red)(4) = 14 - color(red)(4)`

`2y + 0 = 10`

`2y = 10`

`(2y)/color(red)(2) = 10/color(red)(2)`

`(color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2)) = 5`

`y = 5`

Step 3) Substitute `5` for `y` in the solution to the first equation at the end of Step 1 and calculate `x`:

`x = y - 2` becomes:

`x = 5 - 2`

`x = 3`

The solution is: `x = 3` and `y = 5` or `(3, 5)`