We are going to set it up like this... [tex] \left[\begin{array}{ccc}2x-4y=24\\4x-12y=36\end{array}\right] [/tex] Let's take the first part... [tex]2x-4y=24[/tex] Add 4y to both sides. [tex]2x-4y+4y=24+4y[/tex] [tex]2x=24+4y[/tex] Divide both sides by 2. [tex]\frac{2x}{2}=\frac{24+4y}{2}[/tex] [tex]x=2\left(y+6\right)[/tex] Plug that in. [tex]\begin{bmatrix}4\cdot \:2\left(y+6\right)-12y=36\end{bmatrix}[/tex]
Now we are going to isolate y. [tex]4\cdot \:2\left(y+6\right)-12y=36[/tex] Simplify. [tex]8\left(y+6\right)-12y=36[/tex] Expand.. [tex]-4y+48=36[/tex] Subtract 48 from both sides. [tex]-4y+48-48=36-48[/tex] [tex]-4y=-12[/tex] Divide both sides by -4. [tex]\frac{-4y}{-4}=\frac{-12}{-4}[/tex] [tex]y=3[/tex]
[tex]x=2\left(3+6\right)\quad \Rightarrow \quad x=18[/tex] So... The solutions are... [tex]y=3,\:x=18[/tex]
