Question

How do you solve the system of equations `8x + 5y = - 38` and `- 6x + y = 38`?

Answer 1

See a solution process below:

Explanation:

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

`-6x + y = 38`

`color(red)(6x) - 6x + y = color(red)(6x) + 38`

`0 + y = 6x + 38`

`y = 6x + 38`

Step 2) Substitute `6x + 38` for `y` in the first equation and solve for `x`:

`8x + 5y = -38` becomes:

`8x + 5(6x + 38) = -38`

`8x + (5 * 6x) + (5 * 38) = -38`

`8x + 30x + 190 = -38`

`(8 + 30)x + 190 = -38`

`38x + 190 = -38`

`38x + 190 - color(red)(190) = -38 - color(red)(190)`

`38x + 0 = -228`

`38x = -228`

`(38x)/color(red)(38) = -228/color(red)(38)`

`(color(red)(cancel(color(black)(38)))x)/cancel(color(red)(38)) = -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 = 6x + 38` becomes:

`y = (6 xx -6) + 38`

`y = -36 + 38`

`y = 2`

The solution is: `x = -6` and `y = 2` or `(-6, 2)`