Grade 10 Maths · Algebra · Paper 1

Simultaneous Equations Grade 10

Real Simultaneous Equations past paper questions and answers from 2022 to 2025, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

past paper questions: 18 past paper questions
skills: 3 skills
videos: 3 videos

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Question 2.4 · March 2025 · Provincial · 5 marks

2.4 Solve for x and y simultaneously:

x + 3 y = 12

2 x + y = 9

(5)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

Simultaneous Equations skills

Each skill is one thing a memo gives a tick for. Tap one for its own questions, notes and videos.

More Simultaneous Equations Grade 10 questions and answers

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4. Question 3.3 · June 2024 · Paper 1 · Provincial · 4 marks
3.3 Solve simultaneously: $2 x + y = 8$ and $2 y + 3 x = - 2$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Make y the subject of formula in eq 1 $y = 8 - 2 x$ ... (1)
  1 mark · Change the subject of a formula
2. ✓
  Substitute (1) into eq 2 $2 (8 - 2 x) + 3 x = - 2$
  $16 - 4 x + 3 x = - 2$
  1 mark · Solve simultaneous equations by substitution
3. ✓
  Solve for x $- x = - 18$
  $x = 18$
  1 mark · Solve a linear equation
4. ✓
  Substitute x back to find y $y = 8 - 2 (18)$
  $y = - 28$
  1 mark · Solve simultaneous equations by substitution
5. Question 2.3 · November 2024 · Paper 1 · Provincial · 4 marks
2.3 Solve for $x$ and $y$ simultaneously: $y - 3 x = - 2$ and $7 x - 2 y = 8$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Make y the subject in first equation $y = 3 x - 2$
  1 mark · Change the subject of a formula
2. ✓
  Substitute into second equation $7 x - 2 (3 x - 2) = 8$
  $7 x - 6 x + 4 = 8$
  1 mark · Solve simultaneous equations by substitution
3. ✓
  Solve for x $x = 4$
  1 mark · Solve a linear equation
4. ✓
  Solve for y $y = 3 (4) - 2$
  $y = 10$
  1 mark · Solve simultaneous equations by substitution
6. Question 2.3 · March 2024 · Provincial · 5 marks
2.3 Solve for x and y simultaneously if: $x + 3 y - 5 = 0$ and $2 x - 6 y + 2 = 0$ (5)
Show the memo (4 ticks)Memo
1. ✓
  Make x the subject of eq 1 $x = 5 - 3 y$
  1 mark · Change the subject of a formula
2. ✓
  Substitute into eq 2 $2 (5 - 3 y) - 6 y + 2 = 0$
  1 mark · Solve simultaneous equations by substitution
3. ✓
  Solve for y $10 - 6 y - 6 y + 2 = 0$
  $12 - 12 y = 0$
  $y = 1$
  2 marks · Solve a linear equation
4. ✓
  Solve for x $x = 5 - 3 (1) = 2$
  1 mark · Solve simultaneous equations by substitution
7. Question 2.2 · March 2023 · Provincial · 5 marks
2.2 Solve for a and b simultaneously: $a + b = 12$ and $4 a + 2 b = 44$ (5)
Show the memo (5 ticks)Memo
1. ✓
  Make 'a' or 'b' the subject $a = 12 - b$
  1 mark · Change the subject of a formula
2. ✓
  $4 (12 - b) + 2 b = 44$ $4 (12 - b) + 2 b = 44$
  1 mark · Solve simultaneous equations by substitution
3. ✓
  $48 - 4 b + 2 b = 44$ $48 - 4 b + 2 b = 44$
  1 mark · Multiply out a single bracket
4. ✓
  $b = 2$ $- 2 b = - 4$ , so $b = 2$
  1 mark · Solve a linear equation
5. ✓
  $a = 10$ $a = 12 - 2 = 10$
  1 mark · Solve simultaneous equations by substitution
8. Question 2.3 · March 2023 · Provincial · 5 marks
2.3 Solve for x and y simultaneously if:
$x + 3 y + 5 = 0$ and $3 x - 2 y = - 4$ (5)
Show the memo (5 ticks)Memo
1. ✓
  Make x subject of formula $x = - 3 y - 5$
  1 mark · Change the subject of a formula
2. ✓
  Substitute into eq 2 $3 (- 3 y - 5) - 2 y = - 4$
  1 mark · Solve simultaneous equations by substitution
3. ✓
  Simplification $- 9 y - 15 - 2 y = - 4$
  $- 11 y = 11$
  1 mark · Solve a linear equation
4. ✓
  y-value $y = - 1$
  1 mark · Solve a linear equation
5. ✓
  Solve for x $x = - 3 (- 1) - 5 = - 2$
  1 mark · Solve simultaneous equations by substitution
9. Question 3.2 · March 2022 · Provincial · 4 marks
3.2 Solve for x and y simultaneously:
$2 x - y = - 1$ and $x + 2 y = 12$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Make x subject of equation 2 $x = - 2 y + 12$
  1 mark · Change the subject of a formula
2. ✓
  Substitute into equation 1 $2 (- 2 y + 12) - y = - 1$
  $- 4 y + 24 - y = - 1$
  1 mark · Solve simultaneous equations by substitution
3. ✓
  Solve for y $- 5 y = - 25$
  $y = 5$
  1 mark · Solve a linear equation
4. ✓
  Solve for x $x = - 2 (5) + 12$
  $x = 2$
  1 mark · Solve simultaneous equations by substitution
10. Question 3.3 · March 2022 · Provincial · 5 marks
3.3 Solve simultaneously for a and b:
$4 a - b = 5$
$- 3 a + 4 b = 19$ (5)
Show the memo (4 ticks)Memo
1. ✓
  Isolate variable $b = 4 a - 5$ (From eq 1)
  1 mark · Change the subject of a formula
2. ✓
  Substitute $- 3 a + 4 (4 a - 5) = 19$
  $- 3 a + 16 a - 20 = 19$
  1 mark · Solve simultaneous equations by substitution
3. ✓
  Solve for a $13 a = 39 ⟹ a = 3$
  1 mark · Solve a linear equation
4. ✓
  Solve for b $b = 4 (3) - 5 = 7$
  2 marks · Solve simultaneous equations by substitution

Simultaneous Equations Grade 10 videos

Short lessons from South African teachers first. Videos load only when you tap play, to save your data.

Literal Equations Grade 10 Maths Equations PART 1Miss Martins Maths and Science

Simultaneous Equations grade 10 | EliminationKevinmathscience

Simultaneous Equations grade 10 | SubstitutionKevinmathscience

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