Question

How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent `2x + 2y = –6` and `3x – 2y = 11`?

Answer 1

See a solution process below:

Explanation:

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

`2x + 2y = -6`

`2x + 2y - color(red)(2y) = -6 - color(red)(2y)`

`2x + 0 = -6 - 2y`

`2x = -6 - 2y`

`(2x)/color(red)(2) = (-6 - 2y)/color(red)(2)`

`(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = (-6)/color(red)(2) - (2y)/color(red)(2)`

`x = -3 - y`

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

`3x - 2y = 11` becomes:

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

`(3 xx -3) - (3 xx y) - 2y = 11`

`-9 - 3y - 2y = 11`

`-9 - 5y = 11`

`color(red)(9) - 9 - 5y = color(red)(9) + 11`

`0 - 5y = 20`

`-5y = 20`

`(-5y)/color(red)(-5) = 20/color(red)(-5)`

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

`y = -4`

Step 3) Substitute `-4` for `y` in the solution to the first equation at the end of Step 1 and calculate `x`:

`x = -3 - y` becomes:

`x = -3 - (-4)`

`x = -3 + 4`

`x = 1`

The Solution Is: `x = 1` and `y = -4` or `(1, -4)`