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