## Algebra: A Combined Approach (4th Edition)

$\begin{cases} 2x - 3y = 6 \\ -4x + 6y = 12 \end{cases}$ 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.