1. **Problem:** Solve the system of equations: $$y = 3x + 5$$ $$2y = 7x + 2$$ Find the value of $x - y$. 2. **Formula and rules:** To solve a system of linear equations, use substitution or elimination. 3. **Step 1:** From the first equation, $y = 3x + 5$. 4. **Step 2:** Substitute $y$ into the second equation: $$2(3x + 5) = 7x + 2$$ $$6x + 10 = 7x + 2$$ 5. **Step 3:** Rearrange to solve for $x$: $$6x + 10 = 7x + 2$$ $$10 - 2 = 7x - 6x$$ $$8 = x$$ 6. **Step 4:** Substitute $x=8$ back into $y = 3x + 5$: $$y = 3(8) + 5 = 24 + 5 = 29$$ 7. **Step 5:** Calculate $x - y$: $$8 - 29 = -21$$ **Final answer:** $x - y = -21$