1. **State the problem:** Solve the system of equations: $$y = 3x + 5$$ $$2y = 7x + 2$$ Find the value of $x - y$. 2. **Use substitution or elimination:** From the first equation, we have $y = 3x + 5$. 3. **Substitute $y$ into the second equation:** $$2(3x + 5) = 7x + 2$$ 4. **Simplify:** $$6x + 10 = 7x + 2$$ 5. **Solve for $x$:** $$6x + 10 = 7x + 2 \implies 10 - 2 = 7x - 6x \implies 8 = x$$ 6. **Find $y$ using $x=8$:** $$y = 3(8) + 5 = 24 + 5 = 29$$ 7. **Calculate $x - y$:** $$8 - 29 = -21$$ **Final answer:** $x - y = -21$