Question

How do you solve `3x + 3y = - 9; 6x + 2y = 2`?

Answer 1

See a solution process below:

Explanation:

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

`3x +3y = -9`

`(3x +3y)/color(red)(3) = -9/color(red)(3)`

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

`x + y = -3`

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

`x + 0 = -3 - y`

`x = -3 - y`

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

`6x + 2y = 2` becomes:

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

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

`-18 - 6y + 2y = 2`

`-18 + (-6 + 2)y = 2`

`-18 + (-4)y = 2`

`-18 - 4y = 2`

`-18 + color(red)(18) - 4y = 2 + color(red)(18)`

`0 - 4y = 20`

`-4y = 20`

`(-4y)/color(red)(-4) = 20/color(red)(-4)`

`(color(red)(cancel(color(black)(-4)))y)/cancel(color(red)(-4)) = -5`

`y = -5`

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

`x = -3 - y` becomes:

`x = -3 - (-5)`

`x = -3 + 5`

`x = 2`

The Solution Is:

`x = 2` and `y = -5`

Or

`(2, -5)`