# Can you solve this?

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

Jul 20, 2018

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:
$- 3 x + 3 \left(x - 3\right) = 4$

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.

Jul 20, 2018

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

#### Explanation:

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

Equation 2: $- x + y = 3$

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

Equation 1

$3 y = 3 x + 4$

Divide both sides by $3$.

$y = \frac{3 x}{3} + \frac{4}{3}$

$y = x + \frac{4}{3}$

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]}