Question

How do you solve `4x - y = -8` and `x + 3y = -17`?

Answer 1

See a solution process below:

Explanation:

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

`x + 3y = -17`

`x + 3y - color(red)(3y) = -17 - color(red)(3y)`

`x + 0 = -17 - 3y`

`x = -17 - 3y`

Step 2) Substitute `(-17 - 3y)` for `x` in the first equation and solve for `y`:

`4x - y = -8` becomes:

`4(-17 - 3y) - y = -8`

`(4 xx -17) - (4 xx 3y) - y = -8`

`-68 - 12y - 1y = -8`

`-68 + (-12 - 1)y = -8`

`-68 + (-13)y = -8`

`-68 - 13y = -8`

`color(red)(68) - 68 - 13y = color(red)(68) - 8`

`0 - 13y = 60`

`-13y = 60`

`(-13y)/color(red)(-13) = 60/color(red)(-13)`

`(color(red)(cancel(color(black)(-13)))y)/cancel(color(red)(-13)) = -60/13`

`y = -60/13`

Step 3) Substitute `-60/13` for `y` in the solution to the second equation at the end of Step 1 and calculate `y`:

`x = -17 - 3y` becomes:

`x = -17 - (3 * -60/13)`

`x = -17 - (-180/13)`

`x = -17 + 180/13`

`x = (13/13 * -17) + 180/13`

`x = -221/13 + 180/13`

`x = -41/13`

The solution is: `x = -41/13` and `y = -60/13` or `(-41/13, -60/13)`