First [tex]\mathrm{Multiply\:}10x-3y=18\mathrm{\:by\:}3:\quad 30x-9y=54[/tex]
Then [tex]\mathrm{Multiply\:}6x-10y=-22\mathrm{\:by\:}5:\quad 30x-50y=-110[/tex]
To get [tex]\begin{bmatrix}30x-9y=54\\ 30x-50y=-110\end{bmatrix}[/tex]
So...
[tex]30x-50y=-110 \ \textgreater \ \begin{bmatrix}30x-9y=54\\ -41y=-164\end{bmatrix}[/tex]
[tex]-41y=-164 \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}-41 \ \textgreater \ \frac{-41y}{-41}=\frac{-164}{-41}[/tex]
To get y = 4.
[tex]\mathrm{For\:}30x-9y=54\mathrm{\:plug\:in\:} \:y=4 \ \textgreater \ 30x-9\cdot \:4=54[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:9\cdot \:4=36 \ \textgreater \ 30x-36=54 \ \textgreater \ [/tex]
Next [tex]\mathrm{Add\:}36\mathrm{\:to\:both\:sides} \ \textgreater \ 30x-36+36=54+36 \ \textgreater \ \mathrm{Simplify} \ \textgreater \ 30x=90[/tex]
Finally [tex]\mathrm{Divide\:both\:sides\:by\:}30 \ \textgreater \ \frac{30x}{30}=\frac{90}{30} \ \textgreater \ x = 3[/tex]
Therefore our solutions are y = 4, x = 3
