We have [tex]\begin{bmatrix}3x-2y=2\\ 5x-5y=-18\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}3x-2y=2\mathrm{\:by\:}5:\quad 15x-10y=10[/tex]
[tex]\mathrm{Multiply\:}5x-5y=-18\mathrm{\:by\:}3:\quad 15x-15y=-54[/tex]
[tex]\begin{bmatrix}15x-10y=10\\ 15x-15y=-54\end{bmatrix}[/tex]
15x - 15y = -54
-
15x - 10y = 10
/
-5y = -64
[tex]\begin{bmatrix}15x-10y=10\\ -5y=-64\end{bmatrix}[/tex]
[tex]-5y=-64 \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}-5 \ \textgreater \ \frac{-5y}{-5}=\frac{-64}{-5} \ \textgreater \ y=\frac{64}{5}[/tex]
[tex]\mathrm{For\:}15x-10y=10\mathrm{\:plug\:in\:}\ \:y=\frac{64}{5}[/tex]
[tex]15x-10\cdot \frac{64}{5}=10 \ \textgreater \ 10\cdot \frac{64}{5} \ \textgreater \ \mathrm{Multiply\:fractions}:\ \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}[/tex]
[tex]\frac{64\cdot \:10}{5} \ \textgreater \ \mathrm{Multiply\:the\:numbers:}\:64\cdot \:10=640 \ \textgreater \ \frac{640}{5} [/tex]
[tex]\mathrm{Divide\:the\:numbers:}\:\frac{640}{5}=128 \ \textgreater \ 15x-128=10 [/tex]
[tex]\mathrm{Add\:}128\mathrm{\:to\:both\:sides} \ \textgreater \ 15x-128+128=10+128 \ \textgreater \ 15x=138[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}15 \ \textgreater \ \frac{15x}{15}=\frac{138}{15} \ \textgreater \ x=\frac{46}{5}[/tex]
[tex]Therefore\:the\:solutions\:are \ \textgreater \ y=\frac{64}{5},\:x=\frac{46}{5}[/tex]
