Question

How do you solve the following system?: `x + 2y = -2 , x – 3y = -12`

Answer 1

See a solution process below:

Explanation:

Step 1) Solve each equation for `x`:

• Equation 1:

`x + 2y = -2`

`x + 2y - color(red)(2y) = -2 - color(red)(2y)`

`x + 0 = -2 - 2y`

`x = -2 - 2y`

• Equation 2:

`x - 3y = -12`

`x - 3y + color(red)(3y) = -12 + color(red)(3y)`

`x - 0 = -12 + 3y`

`x = -12 + 3y`

Step 2) Because the left side of both equations are the same we can equate the right sides and solve for `y`:

`-2 - 2y = -12 + 3y`

`-2 + color(blue)(12) - 2y + color(red)(2y) = -12 + color(blue)(12) + 3y + color(red)(2y)`

`10 - 0 = 0 + (3 + color(red)(2))y`

`10 = 5y`

`10/color(red)(5) = (5y)/color(red)(5)`

`2 = (color(red)(cancel(color(black)(5)))y)/cancel(color(red)(5))`

`2 = y`

`y = 2`

Step 3) Substitute `2` for `y` in the solutions to either of the equations in Step 1 and calculate `x`:

`x = -12 + 3y` becomes:

`x = -12 + (3 xx 2)`

`x = -12 + 6`

`x = -6`

The Solution Is:

`x = -6` and `y = 2`

Or

`(-6, 2)`