Question 28·Hard·Algebra

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For real constants $a$ and $b$ , the following system of equations has the solution $(3,1)$ .

\begin{aligned} ax+by &= 10 \\[1.4em] bx+ay &= 14 \end{aligned}

If $(p,q)$ is the solution to the following system, what is the value of $p$ ?

\begin{aligned} ap+bq &= 26 \\[1.4em] bp-aq &= 14 \end{aligned}

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