Algebra 2ChallengeSystems of Equations

Systems of Equations · Challenge problem

Three equations, only two unknowns. Solve the first two for $x$ and $y$ , then give the value $r$ must take for the third equation to hold as well.

\begin{aligned} 5 x + y = p \\ 2 x + 3 y = q \\ x + 2 y = r \end{aligned}