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Simultaneous linear equations — KCSE Mathematics

KCSE Mathematics · 85 practice questions · 4 syllabus objectives

29 easy39 medium17 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Solve a system of two simultaneous linear equations by elimination, substitution and graphical methods

Form and solve simultaneous equations from word problems (two unknowns, two conditions)

Determine whether a system of two linear equations has one solution, no solution or infinitely many solutions

Simultaneous linear equations

Sample Questions

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1
easySHORT ANSWER3 marks

Given the simultaneous equations 2x + 3y = 12 and 4x - 6y = 24, state the nature of their solutions. (3 marks)

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Part (a) — 3 marks
The equations are equivalent, representing the same line (1 mk)
There are infinitely many solutions (1 mk)
Any point on the line is a solution (1 mk)
2
easySHORT ANSWER4 marks

Given the equations: x + 2y = 10 and 3x - y = 5, solve for x and y using the substitution method. (4 marks)

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Part (a) — 4 marks
Isolate x in the first equation to express it in terms of y (1 mk)
Substitute the expression for x into the second equation (1 mk)
Solve the resulting equation for y (1 mk)
Substitute back to find x and state both values (1 mk)
3
easySHORT ANSWER4 marks

Solve the simultaneous equations: 3x + 4y = 18 and 2x - y = 1. (4 marks)

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Part (a) — 4 marks
Multiply the second equation by 4 to align coefficients of y (1 mk)
Add the modified second equation to the first to eliminate y (1 mk)
Solve the resulting equation for x (1 mk)
Substitute back to find y and state both values (1 mk)
4

Given the equations 2x + 3y = 12 and 4x + 6y = 24, determine the nature of the solutions for this system. (3 marks)

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Why Practise Simultaneous linear equations?

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