1. **State the problem:** Solve the system of linear equations: $$5p - 5q = 35$$ $$2p - 5q = 26$$ 2. **Write down the system:** $$\begin{cases} 5p - 5q = 35 \\ 2p - 5q = 26 \end{cases}$$ 3. **Subtract the second equation from the first to eliminate $q$: ** $$ (5p - 5q) - (2p - 5q) = 35 - 26 $$ $$ 5p - 5q - 2p + 5q = 9 $$ $$ (5p - 2p) + (-5q + 5q) = 9 $$ $$ 3p + \cancel{0} = 9 $$ $$ 3p = 9 $$ 4. **Solve for $p$: ** $$ p = \frac{9}{3} $$ $$ p = 3 $$ 5. **Substitute $p=3$ into the first equation to find $q$: ** $$ 5(3) - 5q = 35 $$ $$ 15 - 5q = 35 $$ 6. **Isolate $q$: ** $$ -5q = 35 - 15 $$ $$ -5q = 20 $$ $$ q = \frac{20}{-5} $$ $$ q = -4 $$ **Final answer:** $$ p = 3, \quad q = -4 $$ This completes the solution for the first system of equations.