Question

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

Answer 1

See the entire solution process below:

Explanation:

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

`x + 3y = -8`

`x + 3y - color(red)(3y) = -8 - color(red)(3y)`

`x + 0 = -8 - 3y`

`x = -8 - 3y`

Step 2) Substitute `-8 - 3y` for `x` in the first equation and solve for `y`:

`2x + y = 6` becomes:

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

`-16 - 6y + y = 6`

`-16 - 5y = 6`

`color(red)(16) - 16 - 5y = color(red)(16) + 6`

`0 - 5y = 22`

`-5y = 22`

`(-5y)/color(red)(-5) = 22/color(red)(-5)`

`(color(red)(cancel(color(black)(-5)))y)/cancel(color(red)(-5)) = -22/5`

`y = -22/5`

Step 3) Substitute `-22/5` for `y` in the solution to the second equation at the end of Step 1 and calculate `x`:

`x = -8 - 3y` becomes:

`x = -8 - (3 xx -22/5)`

`x = -8 - (-66/5)`

`x = -8 + 66/5`

`x = (5/5 xx -8) + 66/5`

`x = -40/5 + 66/5`

`x = 26/5`

The solution is: `x = 26/5` and `y = -22/5` or `(26/5, -22/5)`