Question A.6: Solve the following two simultaneous equations: (1) 5x + y =...

From (2), we find that x = y + 2. Substitution of this value into (1) gives

\begin{aligned}5(y+2)+y &=-8 \\6 y &=-18 \\y &=-3 \\x &=y+2=-1\end{aligned}

Alternate Solution Multiply each term in (1) by the factor 2 and add the result to (2):

\begin{aligned}10 x+2 y &=-16 \\2 x-2 y &=4 \\\hline 12 x &=-12 \\x &=-1 \\y &=x-2=-3\end{aligned}