Question

Can someone help me find the value of x and the value of y? I need them to show their work, too.

Answer 1

$\bf \begin{cases} x-2y=0\\ 2x-5y=-4 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ x-2y=0\implies x=2y \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting the found \underline{x} in the 2nd equation}}{2(2y)-5y=-4}\implies 4y-5y=-4\implies -y=-4 \\\\\\ y=\cfrac{-4}{-1}\implies \blacktriangleright y=4 \blacktriangleleft \\\\[-0.35em] ~\dotfill$

$\stackrel{\textit{substituting the found \underline{y} in the 1st equation}}{x-2(4)=0}\implies x-8=0\implies \blacktriangleright x=8 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (8,4)~\hfill$