Question

How do you solve the system of equations `4x + 8y = - 20` and `- 10x + 8y = - 6`?

Answer 1

See a solution process below:

Explanation:

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

`4x + 8y = -20`

`(4x + 8y)/color(red)(4) = -20/color(red)(4)`

`(4x)/color(red)(4) + (8y)/color(red)(4) = -5`

`x + 2y = -5`

`x + 2y - color(red)(2y) = -5 - color(red)(2y)`

`x + 0 = -5 - 2y`

`x = -5 - 2y`

Step 2) Substitute `(-5 - 2y)` for `x` in the second equation and solve for `y`:

`-10x + 8y = -6` becomes:

`-10(-5 - 2y) + 8y = -6`

`(-10 * -5) + (-10 * -2y) + 8y = -6`

`50 + 20y + 8y = -6`

`50 + (20 + 8)y = -6`

`50 + 28y = -6`

`-color(red)(50) + 50 + 28y = -color(red)(50) - 6`

`0 + 28y = -56`

`28y = -56`

`(28y)/color(red)(28) = -56/color(red)(28)`

`(color(red)(cancel(color(black)(28)))y)/cancel(color(red)(28)) = -2`

`y = -2`

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

`x = -5 - 2y` becomes:

`x = -5 - (2 * -2)`

`x = -5 - (-4)`

`x = -5 + 4`

`x = -1`

The solution is: `x = -1` and `y = -2` or `(-1, -2)`