[tex]5x-y=10 \\
4x-2y=20 \ \ \ |\hbox{divide both sides by (-2)} \\ \\
5x-y=10 \\
\underline{-2x+y=-10} \ \ \ |\hbox{add by sides} \\
5x-2x-y+y=10-10 \\
3x=0 \\
x=0 \\ \\
\hbox{substitute 0 for x in one of the equations:} \\
5 \times 0 -y=10 \\
-y=10 \\
y=-10 \\ \\
\hbox{the answer:} \\
x=0 \\ y=-10[/tex]
[tex]3x+4y=12 \\
2x-y=-10 \ \ \ |\hbox{multiply both sides by 4} \\ \\
3x+4y=12 \\
\underline{8x-4y=-40} \ \ \ |\hbox{add by sides} \\
3x+8x+4y-4y=12-40 \\
11x=-28 \\
x=-\frac{28}{11} \\
x=-2 \frac{6}{11} \\ \\
\hbox{substitute -28/11 for x in one of the equations:} \\
2 \times (-\frac{28}{11})-y=-10 \\
-\frac{56}{11}-y=-\frac{110}{11} \\
-y=-\frac{110}{11}+\frac{56}{11} \\
-y=-\frac{54}{11} \\
y=\frac{54}{11} \\
y=4 \frac{10}{11} \\ \\
\hbox{the answer:} \\
x=-2\frac{6}{11} \\
y=4 \frac{10}{11}[/tex]
