Question

How do you solve the system of equations `3x + 6y = 6` and `- 3x - 2y = - 14`?

Answer 1

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

Explanation:

Solve the first equation `3x + 6y = 6` for `x` while keeping the equation balanced:

`3x + 6y - 6y = 6 - 6y`

`3x = 6 - 6y`

`(3x)/3 = (6 - 6y)/3`

`x = 6/3 - (6y)/3`

`x = 2 - 2y`

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

`-3(2 - 2y) - 2y = -14`

`-6 + 6y - 2y = -14`

`-6 + 4y = -14`

`6 - 6 + 4y = 6 - 14`

`4y = -8`

`(4y)/4 = -8/4`

`y = -2`

Now that `y` is know substitute `-2` for `y` in the first equation and solve for `x` while keeping the equation balanced:

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

`3x - 12 = 6`

`3x - 12 + 12 = 6 + 12`

`3x = 18`

`(3x)/3 = 18/3`

`x = 6`