Question

Can you solve this?

-3x+3y=4,-x+y=3

Answer 1

First, you have to solve for either `x` or `y`, in this, I would solve for `y` using the second equation.

Add `x` to both sides:
`y=x-3`

Now plug this `y` value into the first equation:
`-3x+3(x-3)=4`

Solve for `x`:
`-9=4`

Since we get an answer that is not possible, there are no solutions to this problem, and the answer is no solution.

Answer 2

Both equations have the same slope, `1`. So they are parallel and there is no solution.

Explanation:

Equation 1: `-3x+3y=4`

Equation 2: `-x+y=3`

Convert both equations into slope-intercept form by solving for `y`.

Equation 1

`3y=3x+4`

Divide both sides by `3`.

`y=(3x)/3+4/3`

`y=x+4/3`

Equation 2

`y=x+3`

Both equations have the same slope, `1`. So they are parallel and there is no solution.

graph{(-3x+3y-4)(-x+y-3)=0 [-10, 10, -5, 5]}