Question

How do you solve the following linear system: #3x + y = -6 , -x + 2y = 8 #?

Answer 1

See the entire solution process below:

Explanation:

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

`3x + y = -6`

`-color(red)(3x) + 3x + y = -color(red)(3x) - 6`

`0 + y = -3x - 6`

`y = -3x - 6`

Step 2) Substitute `-3x - 6` for `y` in the second equation and solve for `x`:

`-x + 2y = 8` becomes:

`-x + 2(-3x - 6) = 8`

`-x - 6x - 12 = 8`

`-7x - 12 = 8`

`-7x - 12 + color(red)(12) = 8 + color(red)(12)`

`-7x - 0 = 20`

`-7x = 20`

`(-7x)/color(red)(-7) = 20/color(red)(-7)`

`(color(red)(cancel(color(black)(-7)))x)/cancel(color(red)(-7)) = -20/7`

`x = -20/7`

Step 3) Substitute `-20/7` for `x` in the solution to the first equation at the end of Step 1 and calculate `y`:

`y = -3x - 6` becomes:

`y = (-3 xx -20/7) - 6`

`y = 60/7 - (6 xx 7/7)`

`y = 60/7 - 42/7`

`y = 18/7`

The solution is: `x = -20/7` and `y = 18/7` or `(-20/7, 18/7)`