1. **State the problem:** Solve the system of equations using substitution and identify the error in the student's solution. Given system: $$5x - y = 15$$ $$7x + y = 21$$ 2. **Express one variable in terms of the other:** From the first equation, $$5x - y = 15 \implies y = 5x - 15$$ 3. **Substitute into the second equation:** Replace $y$ in the second equation with $5x - 15$: $$7x + (5x - 15) = 21$$ 4. **Simplify and solve for $x$:** $$7x + 5x - 15 = 21$$ $$12x - 15 = 21$$ $$12x = 21 + 15$$ $$12x = 36$$ $$x = \frac{36}{12} = 3$$ 5. **Find $y$ using $x=3$:** $$y = 5(3) - 15 = 15 - 15 = 0$$ 6. **Solution set:** The correct solution is $$(x, y) = (3, 0)$$ 7. **Identify the student's error:** The student wrote the solution set as 536, which is incorrect because the solution should be an ordered pair $(x, y)$, not a single number. Possibly, the student concatenated numbers or misread the solution. **Final answer:** The correct solution set is $\boxed{(3, 0)}$.