Question

How do you solve the system of equations `-3x+3y=4` and `-x+y=3`?

Answer 1

See the entire solution process below:

Explanation:

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

`-x + y = 3`

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

`0 + y = x + 3`

`y = x + 3`

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

`-3x + 3y = 4` becomes:

`-3x + 3(x + 3) = 4`

`-3x + (3 * x) + (3 * 3) = 4`

`-3x + 3x + 9 = 4`

`0 + 9 != 4`

`9 != 4`

Because `9` does not equal `4` there is no solution for these two equations which means they are parallel lines, with the same slope and not the same line.