Question

I need help solving for an ordered pair using the substitution and addition methods 4x - 2y = -12 2x +y = -2

Answer 1

`\bf \begin{cases} 4x-2y=-12\\ \cline{1-1} 2x+y=-2\\ \boxed{y}=-2-2x \end{cases}~\hspace{7em}\stackrel{\textit{substituting \underline{y} in the 1st equation}}{4x-2\left( \boxed{-2-2x} \right)=-12}`

`\bf 4x+4+4x=-12\implies 8x+4=-12\implies 8x=-16 \\\\\\ x=\cfrac{-16}{8}\implies \blacktriangleright x=-2 \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that}}{y=-2-2x}\implies y=-2-2(-2)\implies y=-2+4\implies \blacktriangleright y=2 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (-2,2)~\hfill`