The system of equations is solved as follows: 1) x + 2y = 5 and y = 3x - 1 are substituted into each other and simplified 2) This results in 7x = 7, so x = 1 3) Substituting x = 1 into y = 3x - 1 gives y = 2 4) Therefore, the solution is (1, 2).

1. Solve the system of equations:
x + 2y = 5
y = 3x – 1
x + 2(3x – 1) = 5 y = 3x – 1
x + 6x – 2 = 5 y = 3(1) – 1
7x = 7 y=2
x=1 (1, 2)

2. Solve the system of equations:
x + 2y = 5
y = 3x - 1
(1,2)

3. circle and parabola
0 intersections

4. circle and parabola
1 intersection

5. circle and parabola
2 intersections

6. circle and parabola
3 intersections

7. circle and parabola
4 intersections

8. 2 circles
0 intersections

9. 2 circles
1 intersection

10. 2 circles
2 intersections

11. circle and ellipse
0 intersections

12. circle and ellipse
1 intersection

13. circle and ellipse
2 intersections

14. circle and ellipse
3 intersections

15. circle and ellipse
4 intersections

16. Solve the system of equations.
hyperbola
line
4(4 – 8y + 4y2) – 16y2 = 25
16 – 32y + 16y2 – 16y2 = 25

18. Solve the system of equations.
circle y2 = 10 – x2
ellipse if x = 3:
3x2 + 10 – x2 = 28 y2 =10 – (3)2
y2 = 1
2x2 = 18
y= 1
x2 = 9
if x = -3:
x = 3 y2 =10 – (-3)2
y2 = 1
y= 1
Answer: (3, 1), (3, –1) , (–3, 1), and (–3, –1)

19. Answer: (3, 1), (3, –1) , (–3, 1), and (–3, –1)