1. **Problem 4:** Solve the system $$\begin{cases} 2x + y = -3 \\ 2x + 3y = 3 \end{cases}$$ 2. Use elimination by subtracting the first equation from the second: $$ (2x + 3y) - (2x + y) = 3 - (-3) $$ $$ 2x + 3y - 2x - y = 6 $$ $$ 2y = 6 $$ 3. Solve for $y$: $$ y = \frac{\cancel{2}y}{\cancel{2}} = \frac{6}{2} = 3 $$ 4. Substitute $y=3$ into the first equation: $$ 2x + 3 = -3 $$ $$ 2x = -3 - 3 = -6 $$ $$ x = \frac{\cancel{2}x}{\cancel{2}} = \frac{-6}{2} = -3 $$ 5. **Answer for problem 4:** $x = -3$, $y = 3$ --- 6. **Problem 5:** Solve $$\begin{cases} x - 2y = -7 \\ x + y = 5 \end{cases}$$ 7. Use elimination by subtracting the second equation from the first: $$ (x - 2y) - (x + y) = -7 - 5 $$ $$ x - 2y - x - y = -12 $$ $$ -3y = -12 $$ 8. Solve for $y$: $$ y = \frac{\cancel{-3}y}{\cancel{-3}} = \frac{-12}{-3} = 4 $$ 9. Substitute $y=4$ into the second equation: $$ x + 4 = 5 $$ $$ x = 5 - 4 = 1 $$ 10. **Answer for problem 5:** $x = 1$, $y = 4$ --- 11. **Problem 6:** Solve $$\begin{cases} 6x + 4y = 62 \\ 3x + 4y = 47 \end{cases}$$ 12. Subtract the second equation from the first: $$ (6x + 4y) - (3x + 4y) = 62 - 47 $$ $$ 6x + 4y - 3x - 4y = 15 $$ $$ 3x = 15 $$ 13. Solve for $x$: $$ x = \frac{\cancel{3}x}{\cancel{3}} = \frac{15}{3} = 5 $$ 14. Substitute $x=5$ into the second equation: $$ 3(5) + 4y = 47 $$ $$ 15 + 4y = 47 $$ $$ 4y = 47 - 15 = 32 $$ $$ y = \frac{\cancel{4}y}{\cancel{4}} = \frac{32}{4} = 8 $$ 15. **Answer for problem 6:** $x = 5$, $y = 8$ --- 16. **Problem 7:** Solve $$\begin{cases} 3x - 2y = 16 \\ 2x + 2y = 14 \end{cases}$$ 17. Add the two equations to eliminate $y$: $$ (3x - 2y) + (2x + 2y) = 16 + 14 $$ $$ 3x - 2y + 2x + 2y = 30 $$ $$ 5x = 30 $$ 18. Solve for $x$: $$ x = \frac{\cancel{5}x}{\cancel{5}} = \frac{30}{5} = 6 $$ 19. Substitute $x=6$ into the second equation: $$ 2(6) + 2y = 14 $$ $$ 12 + 2y = 14 $$ $$ 2y = 14 - 12 = 2 $$ $$ y = \frac{\cancel{2}y}{\cancel{2}} = \frac{2}{2} = 1 $$ 20. **Answer for problem 7:** $x = 6$, $y = 1$ --- 21. **Problem 8:** Solve $$\begin{cases} 4x + y = 1 \\ 7x - y = -12 \end{cases}$$ 22. Add the two equations to eliminate $y$: $$ (4x + y) + (7x - y) = 1 + (-12) $$ $$ 4x + y + 7x - y = -11 $$ $$ 11x = -11 $$ 23. Solve for $x$: $$ x = \frac{\cancel{11}x}{\cancel{11}} = \frac{-11}{11} = -1 $$ 24. Substitute $x=-1$ into the first equation: $$ 4(-1) + y = 1 $$ $$ -4 + y = 1 $$ $$ y = 1 + 4 = 5 $$ 25. **Answer for problem 8:** $x = -1$, $y = 5$ --- 26. **Problem 9:** Solve $$\begin{cases} 3x + y = 11 \\ 3x - 2y = -4 \end{cases}$$ 27. Subtract the second equation from the first: $$ (3x + y) - (3x - 2y) = 11 - (-4) $$ $$ 3x + y - 3x + 2y = 15 $$ $$ 3y = 15 $$ 28. Solve for $y$: $$ y = \frac{\cancel{3}y}{\cancel{3}} = \frac{15}{3} = 5 $$ 29. Substitute $y=5$ into the first equation: $$ 3x + 5 = 11 $$ $$ 3x = 11 - 5 = 6 $$ $$ x = \frac{\cancel{3}x}{\cancel{3}} = \frac{6}{3} = 2 $$ 30. **Answer for problem 9:** $x = 2$, $y = 5$ --- 31. **Problem 10:** Solve $$\begin{cases} -4x + y = 5 \\ -4x + 4y = 32 \end{cases}$$ 32. Subtract the first equation from the second: $$ (-4x + 4y) - (-4x + y) = 32 - 5 $$ $$ -4x + 4y + 4x - y = 27 $$ $$ 3y = 27 $$ 33. Solve for $y$: $$ y = \frac{\cancel{3}y}{\cancel{3}} = \frac{27}{3} = 9 $$ 34. Substitute $y=9$ into the first equation: $$ -4x + 9 = 5 $$ $$ -4x = 5 - 9 = -4 $$ $$ x = \frac{\cancel{-4}x}{\cancel{-4}} = \frac{-4}{-4} = 1 $$ 35. **Answer for problem 10:** $x = 1$, $y = 9$