Question

Please help!

Solve by substitution.
-x-y-z=-8
-4x+4y+5z=7
2x+2z=4

Answer 1

The third equation gives
\[2x+2z=4\implies x+z=2\implies z=2-x\]Substitute this into the first and second equations to get
\[\begin{cases}-x-y-z=-8\\-4x+4y+5z=7\end{cases}\implies\begin{cases}-x-y-(2-x)=-8\\-4x+4y+5(2-x)=7\end{cases}\]or
\[\begin{cases}-y-2=-8\\-9x+4y+10=7\end{cases}\]The first equation here immediately gives you a solution for \(y\), which you can substitute into this second equation to find \(x\). Then finding \(z\) is easy.