Given that \(a\) and \(b\) are non-zero constants, and that the equations

\[\begin{align*} a^2x+aby&=a+4b\\ abx+b^2y&=a+b \end{align*}\]have an infinite number of solutions for \(x\) and \(y\), express \(a\) in terms of \(b\).

Review question
# If these equations have an infinity of solutions, how are $a$ and $b$ related?

Ref: R6327

Given that \(a\) and \(b\) are non-zero constants, and that the equations

\[\begin{align*} a^2x+aby&=a+4b\\ abx+b^2y&=a+b \end{align*}\]have an infinite number of solutions for \(x\) and \(y\), express \(a\) in terms of \(b\).