Grade 10 Maths · Algebra

Solve simultaneous equations by substitution

Solve two equations together by substituting one into the other (for example putting y = 2x into x + y = 9 gives 3x = 9, so x = 3).

past paper questions use it: 26 past paper questions use it
videos: 4 videos

Learn it: solve simultaneous equations by substitution

Pick one and watch it, then try the questions below. Videos load only when you tap play.

Simultaneous Equations grade 10 | SubstitutionKevinmathscience

Simultaneous Equations grade 10 | Introduction to Elimination and SubstitutionKevinmathscience

Simultaneous Equation - Substitution Grade 10Learn with Mbali

Solving simultaneous equations by substitutionWhiteboard Maths

Now try it on a real exam question

No sign-up. Takes 3 minutes.

Question 3.1 · March 2020 · Provincial · 5 marks

3.1 Solve for x and y simultaneously:

2 x - y = 3

and

3 x + 2 y = 8

(5)

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

More past paper questions: solve simultaneous equations by substitution

Work each one out first, then open the memo and check every tick.

3. Question 3.2.2(b) · May/June 2024 · Paper 1 · National (DBE) · 4 marks
3.2 Given an arithmetic sequence with $T_{1} = 8$ and $T_{2} = 11$ .
A new arithmetic sequence $P$ is formed using the term position and the term value of the given arithmetic sequence. For the new sequence, $P_{8} = 1$ , $P_{11} = 2$ and so forth.
3.2.2(b) Calculate the value of the first term of the new arithmetic sequence.(4)
Show the memo (4 ticks)Memo
1. ✓
  Set up first equation using given sequence data $a + 7 d = 1$
  1 mark · Find a linear general term
2. ✓
  Set up second equation using given sequence data $a + 10 d = 2$
  1 mark · Find a linear general term
3. ✓
  Solve for common difference (d) $3 d = 1 ⟹ d = \frac{1}{3}$
  1 mark · Solve simultaneous equations by elimination
4. ✓
  Solve for first term (a) $a + 7 (\frac{1}{3}) = 1 ⟹ a = - \frac{4}{3}$
  1 mark · Solve simultaneous equations by substitution
4. Question 2.4 · March 2025 · Provincial · 4 marks
2.4 Solve for x and y simultaneously:
$2 x - y = 17$ and $4 y + 3 x = 9$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Make y subject of eq 1 $y = 2 x - 17$
  1 mark · Change the subject of a formula
2. ✓
  Substitute into eq 2 $4 (2 x - 17) + 3 x = 9$
  $8 x - 68 + 3 x = 9$
  1 mark · Solve simultaneous equations by substitution
3. ✓
  Solve for x $11 x = 77 ⟹ x = 7$
  1 mark · Solve a linear equation
4. ✓
  Solve for y $y = 2 (7) - 17 = - 3$
  1 mark · Solve simultaneous equations by substitution
5. 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
6. Question 2.4 · March 2024 · Provincial · 4 marks
2.4 The difference between two numbers is 5. Six times the smaller number is equal to four times the greater number. Find the numbers.(4)
Show the memo (4 ticks)Memo
1. ✓
  Set up equationsLet smaller = x, larger = y.
  $y - x = 5$
  $6 x = 4 y$
  1 mark · Set up an expression or equation
2. ✓
  Substitute $y = x + 5$
  $6 x = 4 (x + 5)$
  1 mark · Solve simultaneous equations by substitution
3. ✓
  Solve for x $6 x = 4 x + 20$
  $2 x = 20$
  $x = 10$
  1 mark · Solve a linear equation
4. ✓
  Solve for y $y = 15$
  1 mark · Solve simultaneous equations by substitution

Free on Android

Know exactly which skill is costing you marks.

Mark past papers tick by tick in the NavyBlue app. It remembers every mark you lose, shows you the skills to fix first, and picks your next questions.

The NavyBlue app showing a learner's weak skills