Question

How do you solve the system of equations `y= - 4x + 17` and `- x - 3y = 4`?

Answer 1

See a solution process below:

Explanation:

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

`-x - 3y + color(red)(3y) = 4 + color(red)(3y)`

`-x - 0 = 4 + 3y`

`-x = 4 + 3y`

`color(red)(-1) xx -x = color(red)(-1)(4 + 3y)`

`x = (color(red)(-1) xx 4) + (color(red)(-1) xx 3y)`

`x = -4 - 3y`

Step 2) Substitute `(-4 - 3y)` for `x` in the first equation and solve for `y`:

`y = -4x + 17` becomes:

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

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

`y = 16 + 12y + 17`

`y = 16 + 17 + 12y`

`y = 33 + 12y`

`y - color(red)(12y) = 33 + 12y - color(red)(12y)`

`1y - color(red)(12y) = 33 + 0`

`(1 - color(red)(12))y = 33`

`-11y = 33`

`(-11y)/color(red)(-11) = 33/color(red)(-11)`

`(color(red)(cancel(color(black)(-11)))y)/cancel(color(red)(-11)) = -3`

`y = -3`

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

`x = -4 - 3y` becomes:

`x = -4 - (3 xx -3)`

`x = -4 - (-9)`

`x = -4 + 9`

`x = 5`

The Solution Is: `x = 5` and `y = -3` or `(5, -3)`