Question

How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent `y = -x - 4` and `y = x + 2`?

Answer 1

See a solution process below:

Explanation:

Step 1) Because the first equation is already solved for `y` we can substitute `(-x - 4)` from `y` in the second equation and solve for `x`:

`y = x + 2` becomes:

`-x - 4 = x + 2`

`color(red)(x) - x - 4 - color(blue)(2) = color(red)(x) + x + 2 - color(blue)(2)`

`0 - 6 = color(red)(1x) + 1x + 0`

`-6 = 2x`

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

`-3 = (color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2))`

`-3 = x`

`x = -3`

Step 2) Substitute `-3` for `x` in the first equation and calculate `y`:

`y = -x - 4` becomes:

`y = -(-3) - 4`

`y = 3 - 4`

`y = -1`

The solution is: `x = -3` and `y = -1` or `(-3, -1)`