Simultaneous Equations Quiz

1. Solve: x + y = 7 and x − y = 3

1. x = 2, y = 5
2. x = 3, y = 4
3. x = 4, y = 3
4. x = 5, y = 2

2. Solve: 2x + y = 10 and x + y = 6

1. x = 2, y = 4
2. x = 3, y = 4
3. x = 4, y = 2
4. x = 5, y = 0

3. What does it mean graphically when two linear simultaneous equations have no solution?

1. The lines are parallel and never meet
2. The lines are perpendicular
3. The lines are the same line
4. The lines cross at the origin

4. Solve by substitution: y = 2x + 1 and 3x + y = 16

1. x = 2, y = 5
2. x = 3, y = 7
3. x = 4, y = 9
4. x = 5, y = 11

5. Solve: 3x + 2y = 12 and x − y = 1

1. x = 14/5, y = 9/5
2. x = 2, y = 3
3. x = 3, y = 2
4. x = 4, y = 0

6. Solve by elimination: 4x + 3y = 21 and 2x − 3y = 3

1. x = 2, y = 3
2. x = 3, y = 3
3. x = 4, y = 3
4. x = 4, y = 5/3

7. A cinema sells adult tickets for £9 and child tickets for £5. 50 tickets are sold for a total of £330. How many adult tickets were sold?

1. 15
2. 20
3. 25
4. 30

8. Solve: 5x + 2y = 16 and 3x + 2y = 12

1. x = 1, y = 5
2. x = 2, y = 3
3. x = 3, y = 2
4. x = 4, y = −2

9. How many solutions do simultaneous equations have if the two lines are identical (same equation)?

1. Exactly one
2. Exactly two
3. Infinitely many
4. None

10. Solve the simultaneous equations: y = x² and y = x + 2

1. x = −2 or x = 1
2. x = 0 or x = 2
3. x = 1 or x = 2
4. x = 2 or x = −1

11. Solve: 2x + 5y = 19 and 2x + 3y = 11

1. x = −2, y = 5
2. x = 1, y = 4
3. x = 2, y = 3
4. x = 3, y = 2

12. Solve: x + 2y = 8 and 3x − y = 3

1. x = 1, y = 3
2. x = 2, y = 3
3. x = 3, y = 2
4. x = 4, y = 2

13. Two numbers sum to 15 and their difference is 3. What are the numbers?

1. 10 and 5
2. 12 and 3
3. 8 and 7
4. 9 and 6

14. Solve: 4x − y = 5 and 2x + 3y = 13

1. x = 1, y = −1
2. x = 2, y = 3
3. x = 2.5, y = 5
4. x = 3, y = 2

15. The sum of two numbers is 20 and one is three times the other. What is the smaller number?

1. 4
2. 5
3. 6
4. 8

16. Solve: 3x + 4y = 24 and 6x − 4y = 12

1. x = 2, y = 4.5
2. x = 3, y = 4
3. x = 4, y = 3
4. x = 6, y = 1.5

17. Which method is best when one equation already has y isolated (e.g. y = 3x − 1)?

1. Elimination
2. Graphical method
3. Substitution
4. Trial and improvement

18. Solve: 5x + y = 14 and y = 2x

1. x = 1, y = 2
2. x = 2, y = 4
3. x = 3, y = 6
4. x = 4, y = 8

19. Solve simultaneously: x + y = 5 and x² + y² = 13

1. x = −2, y = 7
2. x = 2, y = 3 or x = 3, y = 2
3. x = 4, y = 1 or x = 1, y = 4
4. x = 5, y = 0 or x = 0, y = 5

20. Solve: 7x − 3y = 22 and 5x + 3y = 26

1. x = 2, y = −8/3
2. x = 3, y = −1/3
3. x = 4, y = 2
4. x = 5, y = 3