Question

How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent `x – 2y = 8` and `x + y = –1`?

Answer 1

See a solution process below:

Explanation:

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

`x - 2y = 8`

`x - 2y + color(red)(2y) = 8 + color(red)(2y)`

`x - 0 = 8 + 2y`

`x = 8 + 2y`

Step 2) Substitute `(8 + 2y)` for `x` in the second equation and solve for `y`:

`x + y = -1` becomes:

`(8 + 2y) + y = -1`

`8 + 2y + 1y = -1`

`8 + (2 + 1)y = -1`

`8 + 3y = -1`

`-color(red)(8) + 8 + 3y = -color(red)(8) - 1`

`0 + 3y = -9`

`3y = -9`

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

`(color(red)(cancel(color(black)(3)))y)/cancel(color(red)(3)) = -3`

`y = -3`

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

`x = 8 + 2y` becomes:

`x = 8 + (2 * -3)`

`x = 8 + (-6)`

`x = 2`

The solution is: `x = 2` and `y = -3` or `(2, -3)`

Because there is at least one point in common these equations are consistent.