Success Homeschool

Year 11 Mathematics · Simultaneous linear equations

Name: ______________________

Date: ____________

1. The lines y = x + 1 and y = 3x − 3 intersect at which point?
- ☐ (a) (1, 2)
- ☐ (b) (2, 3)
- ☐ (c) (3, 4)
- ☐ (d) (0, 1)
2. Solve x + y = 12 and x − y = 2. What is the value of x?
3. Solve y = 2x and x + y = 9. What is the value of y?
4. What is the best first step to solve 2x + 3y = 13 and 2x + y = 7 by elimination?
- ☐ (a) Add the two equations
- ☐ (b) Subtract the second equation from the first to eliminate x
- ☐ (c) Multiply both equations by 0
- ☐ (d) Divide the first equation by 3
5. How many solutions does the pair y = 2x + 1 and y = 2x − 4 have?
- ☐ (a) None
- ☐ (b) Exactly one
- ☐ (c) Exactly two
- ☐ (d) Infinitely many
6. Solve 3x + 2y = 16 and x − 2y = 0. What is the value of y?
7. Two numbers add to 20 and their difference is 6. What is the larger number?
8. Two pens and one notebook cost $7. One pen and one notebook cost $5. How much does one pen cost?

Answer sheet

1. (2, 3) — x + 1 = 3x − 3 gives 4 = 2x, so x = 2 and y = 3. Check: 3 × 2 − 3 = 3.
2. x = 7 — Adding the equations gives 2x = 14, so x = 7 (and y = 5).
3. y = 6 — Substitute: x + 2x = 9, so x = 3 and y = 2 × 3 = 6.
4. Subtract the second equation from the first to eliminate x — Both equations contain 2x, so subtracting removes x: 2y = 6, giving y = 3 and then x = 2.
5. None — Both lines have gradient 2 but different y-intercepts, so they are parallel and never meet.
6. y = 2 — Adding the equations gives 4x = 16, so x = 4. Then 4 − 2y = 0, so y = 2.
7. 13 — x + y = 20 and x − y = 6. Adding gives 2x = 26, so x = 13 and y = 7.
8. $2 — Subtracting the equations (2p + n) − (p + n) = 7 − 5 gives p = 2. So a pen costs $2 and a notebook costs $3.