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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.
Worksheet StudioPractice pack · Ages 16-18
Simultaneous linear equations
Take your time. Show your thinking.
1. Solve the simultaneous equations x + y = 20 and x − y = 12. Find the value of x.
2. Solve the simultaneous equations x + y = 39 and x − y = 7. Find the value of x.
3. Solve the simultaneous equations x + y = 10 and x − y = 4. Find the value of x.
4. Solve the simultaneous equations x + y = 14 and x − y = 6. Find the value of x.
5. Solve the simultaneous equations x + y = 28 and x − y = 10. Find the value of x.
6. Solve the simultaneous equations x + y = 31 and x − y = 3. Find the value of x.
7. Solve the simultaneous equations x + y = 31 and x − y = 5. Find the value of x.
8. Solve the simultaneous equations x + y = 14 and x − y = 10. Find the value of x.
9. Solve the simultaneous equations x + y = 10 and x − y = 2. Find the value of x.
10. Solve the simultaneous equations x + y = 46 and x − y = 4. Find the value of x.
11. Solve the simultaneous equations x + y = 38 and x − y = 4. Find the value of x.
12. Solve the simultaneous equations x + y = 33 and x − y = 13. Find the value of x.
12 questions · Seed 104744 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 16-18
Simultaneous linear equations
Answers and reasoning. Review before teaching.
1. Solve the simultaneous equations x + y = 20 and x − y = 12. Find the value of x.
16Add the two equations: 2x = 20 + 12 = 32, so x = 16 (and y = 4).
2. Solve the simultaneous equations x + y = 39 and x − y = 7. Find the value of x.
23Add the two equations: 2x = 39 + 7 = 46, so x = 23 (and y = 16).
3. Solve the simultaneous equations x + y = 10 and x − y = 4. Find the value of x.
7Add the two equations: 2x = 10 + 4 = 14, so x = 7 (and y = 3).
4. Solve the simultaneous equations x + y = 14 and x − y = 6. Find the value of x.
10Add the two equations: 2x = 14 + 6 = 20, so x = 10 (and y = 4).
5. Solve the simultaneous equations x + y = 28 and x − y = 10. Find the value of x.
19Add the two equations: 2x = 28 + 10 = 38, so x = 19 (and y = 9).
6. Solve the simultaneous equations x + y = 31 and x − y = 3. Find the value of x.
17Add the two equations: 2x = 31 + 3 = 34, so x = 17 (and y = 14).
7. Solve the simultaneous equations x + y = 31 and x − y = 5. Find the value of x.
18Add the two equations: 2x = 31 + 5 = 36, so x = 18 (and y = 13).
8. Solve the simultaneous equations x + y = 14 and x − y = 10. Find the value of x.
12Add the two equations: 2x = 14 + 10 = 24, so x = 12 (and y = 2).
9. Solve the simultaneous equations x + y = 10 and x − y = 2. Find the value of x.
6Add the two equations: 2x = 10 + 2 = 12, so x = 6 (and y = 4).
10. Solve the simultaneous equations x + y = 46 and x − y = 4. Find the value of x.
25Add the two equations: 2x = 46 + 4 = 50, so x = 25 (and y = 21).
11. Solve the simultaneous equations x + y = 38 and x − y = 4. Find the value of x.
21Add the two equations: 2x = 38 + 4 = 42, so x = 21 (and y = 17).
12. Solve the simultaneous equations x + y = 33 and x − y = 13. Find the value of x.
23Add the two equations: 2x = 33 + 13 = 46, so x = 23 (and y = 10).
12 questions · Seed 104744 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18
Simultaneous linear equations
Take your time. Show your thinking.
1. Solve the simultaneous equations x + y = 20 and x − y = 12. Find the value of x.
2. Solve the simultaneous equations x + y = 39 and x − y = 7. Find the value of x.
3. Solve the simultaneous equations x + y = 10 and x − y = 4. Find the value of x.
4. Solve the simultaneous equations x + y = 14 and x − y = 6. Find the value of x.
5. Solve the simultaneous equations x + y = 28 and x − y = 10. Find the value of x.
6. Solve the simultaneous equations x + y = 31 and x − y = 3. Find the value of x.
7. Solve the simultaneous equations x + y = 31 and x − y = 5. Find the value of x.
8. Solve the simultaneous equations x + y = 14 and x − y = 10. Find the value of x.
9. Solve the simultaneous equations x + y = 10 and x − y = 2. Find the value of x.
10. Solve the simultaneous equations x + y = 46 and x − y = 4. Find the value of x.
11. Solve the simultaneous equations x + y = 38 and x − y = 4. Find the value of x.
12. Solve the simultaneous equations x + y = 33 and x − y = 13. Find the value of x.
12 questions · Seed 104744 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18
Simultaneous linear equations
Answers and reasoning. Review before teaching.
1. Solve the simultaneous equations x + y = 20 and x − y = 12. Find the value of x.
16Add the two equations: 2x = 20 + 12 = 32, so x = 16 (and y = 4).
2. Solve the simultaneous equations x + y = 39 and x − y = 7. Find the value of x.
23Add the two equations: 2x = 39 + 7 = 46, so x = 23 (and y = 16).
3. Solve the simultaneous equations x + y = 10 and x − y = 4. Find the value of x.
7Add the two equations: 2x = 10 + 4 = 14, so x = 7 (and y = 3).
4. Solve the simultaneous equations x + y = 14 and x − y = 6. Find the value of x.
10Add the two equations: 2x = 14 + 6 = 20, so x = 10 (and y = 4).
5. Solve the simultaneous equations x + y = 28 and x − y = 10. Find the value of x.
19Add the two equations: 2x = 28 + 10 = 38, so x = 19 (and y = 9).
6. Solve the simultaneous equations x + y = 31 and x − y = 3. Find the value of x.
17Add the two equations: 2x = 31 + 3 = 34, so x = 17 (and y = 14).
7. Solve the simultaneous equations x + y = 31 and x − y = 5. Find the value of x.
18Add the two equations: 2x = 31 + 5 = 36, so x = 18 (and y = 13).
8. Solve the simultaneous equations x + y = 14 and x − y = 10. Find the value of x.
12Add the two equations: 2x = 14 + 10 = 24, so x = 12 (and y = 2).
9. Solve the simultaneous equations x + y = 10 and x − y = 2. Find the value of x.
6Add the two equations: 2x = 10 + 2 = 12, so x = 6 (and y = 4).
10. Solve the simultaneous equations x + y = 46 and x − y = 4. Find the value of x.
25Add the two equations: 2x = 46 + 4 = 50, so x = 25 (and y = 21).
11. Solve the simultaneous equations x + y = 38 and x − y = 4. Find the value of x.
21Add the two equations: 2x = 38 + 4 = 42, so x = 21 (and y = 17).
12. Solve the simultaneous equations x + y = 33 and x − y = 13. Find the value of x.
23Add the two equations: 2x = 33 + 13 = 46, so x = 23 (and y = 10).
12 questions · Seed 104744 · Age guidance, not curriculum certification