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Maths Lab · Free lesson · 22 minutes

Two equations, one common solution

Use elimination and substitution to find a pair that satisfies two equations and verify both conditions.

JSS3 · simultaneous equations

01 · Think first

Start with a question.

Two numbers total 18 and differ by 4. A pair that matches just the total is not enough: it must match the difference too.

What you already know
  • Solve a two-step linear equation
  • Add signed numbers
  • Substitute an expression for a variable
The pair (6, 3) satisfies x + y = 9. Does it also satisfy x − y = 1?

02 · See it

Check both rows

One candidate can satisfy the first row and fail the second. The common solution is the intersection of both constraints.

Condition 1
x + y = 18
Condition 2
x − y = 4
Add corresponding sides
2x = 22
Common pair
(x, y) = (11, 7)

Use the justified worked steps below to explore this idea.

03 · Show steps · explain why

One justified step at a time.

  1. 1

    x + y = 18 and x − y = 4

    Each statement describes a condition on the same two unknowns.

04 · Mistake clinic

Find the first wrong idea.

Tempting wrong line

2x + y = 11 and x − y = 1 → subtract: x = 10.

Compare the correction and its reason

Subtracting gives x + 2y = 10. Adding eliminates y: 3x = 12, so x = 4 and y = 3.

A minus sign acts on every term of the second equation. y − (−y) is 2y, not zero.

Check: Write parentheses around a whole row before subtracting and verify the proposed pair in both equations.

A mistake is evidence about the next idea to repair. It is not a label for the learner.

05 · Your turn

Try first. Then use a hint.

1. Solve x + y = 12 and x − y = 4. Enter x.guided practice
2. y = 3x − 2 and x + y = 14. Enter y.independent practice
3. Two pens and one notebook cost ₦1,000. One pen and one notebook cost ₦700. Find the notebook price in naira.far practice

06 · Check & reflect → next step

Understanding includes explaining.

Why must a pair satisfy both equations? Explain the cancellation rather than only giving a result.

Choose your next learning need

Revisit the graph lesson to interpret the common pair as an intersection, then practise less obvious coefficients.

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Source and review status

JEM-J3-M04-002 · Phase 3C JSS3-BECE Mathematics REPAIRED · Lesson 5 · printed pp. 17–18

This published free lesson contains selected explanations and authored practice. Complete canonical volumes and tutor solutions remain in the protected Content Vault.