Question

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

Answer 1

See the solution process below:

Explanation:

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

`3x + 3y = -3`

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

`(3x)/color(red)(3) + (3y)/color(red)(3) = -1`

`x + y = -1`

`x + y - color(red)(y) = -1 - color(red)(y)`

`x + 0 = -1 - y`

`x = -1 - y`

Step 2) Substitute `-1 - y` for `x` in the second equation and solve for `y`:

`2x + 2y = 6` becomes:

`2(-1 - y) + 2y = 6`

`(2 * -1) - (2 * y) + 2y = 6`

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

`-2 - 0 = 6`

`-2 != 6`

Because `-2` is not equal to `6` there is no solution to this problem.

It means these two lines are parallel and are NOT the same line and therefore there is no place the two lines intersect.