1. **Problem (a): Solve the system by substitution:** Given: $$2x + y = 7$$ $$x - 2y = 6$$ 2. Solve the first equation for $y$: $$y = 7 - 2x$$ 3. Substitute $y = 7 - 2x$ into the second equation: $$x - 2(7 - 2x) = 6$$ 4. Simplify and solve for $x$: $$x - 14 + 4x = 6$$ $$5x - 14 = 6$$ $$5x = 20$$ $$x = 4$$ 5. Substitute $x = 4$ back into $y = 7 - 2x$: $$y = 7 - 2(4) = 7 - 8 = -1$$ 6. **Solution for (a):** $$x = 4, y = -1$$ --- 7. **Problem (b): Solve the system by substitution:** Given: $$x - 2y = -2$$ $$3x + 2y = 34$$ 8. Solve the first equation for $x$: $$x = -2 + 2y$$ 9. Substitute $x = -2 + 2y$ into the second equation: $$3(-2 + 2y) + 2y = 34$$ 10. Simplify and solve for $y$: $$-6 + 6y + 2y = 34$$ $$8y - 6 = 34$$ $$8y = 40$$ $$y = 5$$ 11. Substitute $y = 5$ back into $x = -2 + 2y$: $$x = -2 + 2(5) = -2 + 10 = 8$$ 12. **Solution for (b):** $$x = 8, y = 5$$