Answer
no solutions
Work Step by Step
$\begin{cases} 2x - 3y = 6 \\ -4x + 6y = 12 \end{cases}$
We solve for x from the first equation:
$2x-3y=6$
$2x=6+3y$
$x=3+\frac{3}{2}y$
Now that we have a solution for x, we substitute $x=3+\frac{3}{2}y$ in the second equation:
$-4x + 6y = 12 $
$-4(3+\frac{3}{2}y) + 6y = 12 $
$-12-6y + 6y = 12 $
$-12 = 12 $
Since this statement is never true, the equation has no solutions.
