MathsAges 13-15

Simultaneous linear equations

Eliminate y by adding x + y and x − y to solve a pair of simultaneous linear equations. Review suitability for your learners before teaching.

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Age band:Ages 13-15 Ages 16-18

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Worksheet StudioPractice pack · Ages 13-15

Simultaneous linear equations

Take your time. Show your thinking.

1. Solve the simultaneous equations x + y = 16 and x − y = 10. Find the value of x.
16 · 10 · Simultaneous linear equati…
2. Solve the simultaneous equations x + y = 26 and x − y = 8. Find the value of x.
26 · 8 · Simultaneous linear equati…
3. Solve the simultaneous equations x + y = 16 and x − y = 8. Find the value of x.
16 · 8 · Simultaneous linear equati…
4. Solve the simultaneous equations x + y = 23 and x − y = 17. Find the value of x.
23 · 17 · Simultaneous linear equati…
5. Solve the simultaneous equations x + y = 25 and x − y = 19. Find the value of x.
25 · 19 · Simultaneous linear equati…
6. Solve the simultaneous equations x + y = 24 and x − y = 6. Find the value of x.
24 · 6 · Simultaneous linear equati…
7. Solve the simultaneous equations x + y = 27 and x − y = 3. Find the value of x.
27 · 3 · Simultaneous linear equati…
8. Solve the simultaneous equations x + y = 15 and x − y = 11. Find the value of x.
15 · 11 · Simultaneous linear equati…
9. Solve the simultaneous equations x + y = 32 and x − y = 10. Find the value of x.
32 · 10 · Simultaneous linear equati…
10. Solve the simultaneous equations x + y = 27 and x − y = 21. Find the value of x.
27 · 21 · Simultaneous linear equati…
11. Solve the simultaneous equations x + y = 17 and x − y = 9. Find the value of x.
17 · 9 · Simultaneous linear equati…
12. Solve the simultaneous equations x + y = 24 and x − y = 10. Find the value of x.
24 · 10 · Simultaneous linear equati…

12 questions · Seed 104734 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

Simultaneous linear equations

Answers and reasoning. Review before teaching.

1. Solve the simultaneous equations x + y = 16 and x − y = 10. Find the value of x.
13
Add the two equations: 2x = 16 + 10 = 26, so x = 13 (and y = 3).
2. Solve the simultaneous equations x + y = 26 and x − y = 8. Find the value of x.
17
Add the two equations: 2x = 26 + 8 = 34, so x = 17 (and y = 9).
3. Solve the simultaneous equations x + y = 16 and x − y = 8. Find the value of x.
12
Add the two equations: 2x = 16 + 8 = 24, so x = 12 (and y = 4).
4. Solve the simultaneous equations x + y = 23 and x − y = 17. Find the value of x.
20
Add the two equations: 2x = 23 + 17 = 40, so x = 20 (and y = 3).
5. Solve the simultaneous equations x + y = 25 and x − y = 19. Find the value of x.
22
Add the two equations: 2x = 25 + 19 = 44, so x = 22 (and y = 3).
6. Solve the simultaneous equations x + y = 24 and x − y = 6. Find the value of x.
15
Add the two equations: 2x = 24 + 6 = 30, so x = 15 (and y = 9).
7. Solve the simultaneous equations x + y = 27 and x − y = 3. Find the value of x.
15
Add the two equations: 2x = 27 + 3 = 30, so x = 15 (and y = 12).
8. Solve the simultaneous equations x + y = 15 and x − y = 11. Find the value of x.
13
Add the two equations: 2x = 15 + 11 = 26, so x = 13 (and y = 2).
9. Solve the simultaneous equations x + y = 32 and x − y = 10. Find the value of x.
21
Add the two equations: 2x = 32 + 10 = 42, so x = 21 (and y = 11).
10. Solve the simultaneous equations x + y = 27 and x − y = 21. Find the value of x.
24
Add the two equations: 2x = 27 + 21 = 48, so x = 24 (and y = 3).
11. Solve the simultaneous equations x + y = 17 and x − y = 9. Find the value of x.
13
Add the two equations: 2x = 17 + 9 = 26, so x = 13 (and y = 4).
12. Solve the simultaneous equations x + y = 24 and x − y = 10. Find the value of x.
17
Add the two equations: 2x = 24 + 10 = 34, so x = 17 (and y = 7).

12 questions · Seed 104734 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Simultaneous linear equations

Take your time. Show your thinking.

1. Solve the simultaneous equations x + y = 16 and x − y = 10. Find the value of x.
16 · 10 · Simultaneous linear equati…
2. Solve the simultaneous equations x + y = 26 and x − y = 8. Find the value of x.
26 · 8 · Simultaneous linear equati…
3. Solve the simultaneous equations x + y = 16 and x − y = 8. Find the value of x.
16 · 8 · Simultaneous linear equati…
4. Solve the simultaneous equations x + y = 23 and x − y = 17. Find the value of x.
23 · 17 · Simultaneous linear equati…
5. Solve the simultaneous equations x + y = 25 and x − y = 19. Find the value of x.
25 · 19 · Simultaneous linear equati…
6. Solve the simultaneous equations x + y = 24 and x − y = 6. Find the value of x.
24 · 6 · Simultaneous linear equati…
7. Solve the simultaneous equations x + y = 27 and x − y = 3. Find the value of x.
27 · 3 · Simultaneous linear equati…
8. Solve the simultaneous equations x + y = 15 and x − y = 11. Find the value of x.
15 · 11 · Simultaneous linear equati…
9. Solve the simultaneous equations x + y = 32 and x − y = 10. Find the value of x.
32 · 10 · Simultaneous linear equati…
10. Solve the simultaneous equations x + y = 27 and x − y = 21. Find the value of x.
27 · 21 · Simultaneous linear equati…
11. Solve the simultaneous equations x + y = 17 and x − y = 9. Find the value of x.
17 · 9 · Simultaneous linear equati…
12. Solve the simultaneous equations x + y = 24 and x − y = 10. Find the value of x.
24 · 10 · Simultaneous linear equati…

12 questions · Seed 104734 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Simultaneous linear equations

Answers and reasoning. Review before teaching.

1. Solve the simultaneous equations x + y = 16 and x − y = 10. Find the value of x.
13
Add the two equations: 2x = 16 + 10 = 26, so x = 13 (and y = 3).
2. Solve the simultaneous equations x + y = 26 and x − y = 8. Find the value of x.
17
Add the two equations: 2x = 26 + 8 = 34, so x = 17 (and y = 9).
3. Solve the simultaneous equations x + y = 16 and x − y = 8. Find the value of x.
12
Add the two equations: 2x = 16 + 8 = 24, so x = 12 (and y = 4).
4. Solve the simultaneous equations x + y = 23 and x − y = 17. Find the value of x.
20
Add the two equations: 2x = 23 + 17 = 40, so x = 20 (and y = 3).
5. Solve the simultaneous equations x + y = 25 and x − y = 19. Find the value of x.
22
Add the two equations: 2x = 25 + 19 = 44, so x = 22 (and y = 3).
6. Solve the simultaneous equations x + y = 24 and x − y = 6. Find the value of x.
15
Add the two equations: 2x = 24 + 6 = 30, so x = 15 (and y = 9).
7. Solve the simultaneous equations x + y = 27 and x − y = 3. Find the value of x.
15
Add the two equations: 2x = 27 + 3 = 30, so x = 15 (and y = 12).
8. Solve the simultaneous equations x + y = 15 and x − y = 11. Find the value of x.
13
Add the two equations: 2x = 15 + 11 = 26, so x = 13 (and y = 2).
9. Solve the simultaneous equations x + y = 32 and x − y = 10. Find the value of x.
21
Add the two equations: 2x = 32 + 10 = 42, so x = 21 (and y = 11).
10. Solve the simultaneous equations x + y = 27 and x − y = 21. Find the value of x.
24
Add the two equations: 2x = 27 + 21 = 48, so x = 24 (and y = 3).
11. Solve the simultaneous equations x + y = 17 and x − y = 9. Find the value of x.
13
Add the two equations: 2x = 17 + 9 = 26, so x = 13 (and y = 4).
12. Solve the simultaneous equations x + y = 24 and x − y = 10. Find the value of x.
17
Add the two equations: 2x = 24 + 10 = 34, so x = 17 (and y = 7).

12 questions · Seed 104734 · Age guidance, not curriculum certification