Question

How do you solve the system of equations `2x + 4y = - 22` and `3x + 3y = - 21`?

Answer 1

`x = -3 and`y = -4#

Explanation:

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

`2x + 4y - 4y = -22 - 4y`

`2x + 0 = -22 - 4y`

`2x = -22 - 4y`

`(2x)/2 = (-22)/2 - (4y)/2`

`x = -11 - 2y`

Step 2) Substitute `-11 - 2y` for `x` in the second equation and solve for `y`:

`3(-11 - 2y) + 3y = -21`

`-33 - 6y + 3y = -21`

`-33 - 3y = -21`

`-33 + 33 - 3y = -21 + 33`

`-3y = 12`

`(-3y)/(-3) = 12/(-3)`

`y = -4`

Step 3) Substitute `18` for `y` in the solution to the first equation in Step 1) and calculate `x`:

`x = -11 - (2*-4)`

`x = -11 + 8`

`x = -3`