Question

How do you solve the system of equations `-4x - 12y = - 16` and `- 3x + 3y = 12`?

Answer 1

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

Explanation:

Step 1) Solve the first equation for `x` while keeping the equation balanced:

`-4x - 12y + 12y = -16 + 12y`

`-4x = -16 + 12y`

`(-4x)/-4 = (-16 + 12y)/-4`

`x = (-16)/-4 + (12y)/-4`

`x = 4 - 3y`

Step 2) Substitute `4 - 3y` for `x` in the second equation and solve for `x` while keeping the equation balanced:

`-3(4 - 3y) + 3y = 12`

`-12 + 9y + 3y = 12`

`-12 + 12y = 12`

`-12 + 12y + 12 = 12 + 12`

`12y = 24`

`(12y)/12 = 24/12`

`y = 2`

Step 3) Substitute `2` for `y` in the solution for the first equation and calculate `x`:

`x = 4 - (3*2)`

`x = 4 - 6`

`x = -2`