[tex]\begin{cases}-2x+3y=9{} \\ 4x+3y=-9{}\end{cases}[/tex]
As we can see the y coefficients are the same for both equations, then let's SUBCTRAC both equations
[tex]\begin{gathered} (-2x+3y)-(4x+3y)=9-(-9) \\ \\ -2x+3y-4x-3y=9+9 \\ \\ -6x=18 \\ \\ x=-\frac{18}{6}=-3 \end{gathered}[/tex]
Now we have the value of x we can use any of the equations to find y, I'll use the first one
[tex]\begin{gathered} -2\cdot(-3)+3y=9 \\ \\ 6+3y=9 \\ \\ 3y=9-6 \\ \\ 3y=3 \\ \\ y=1 \end{gathered}[/tex]
Therefore the solution is
[tex](-3,1)[/tex]
x = -3 and y = 1
