Simultaneous equations & inequalities

Senior High 6 questions

What simultaneous equations & inequalities means

You learn to find unknown values from two or more simple algebra statements. This helps you handle linked equations and decide which values satisfy a condition.

What you will practise

Solve two linear equations by adding or subtracting
Use substitution when one equation already gives a value
Work out which values make a linear inequality true
Check answers by putting them back into the equations

Before you start

You should already be comfortable with basic algebra, collecting like terms, and solving one-step and two-step equations. You also need to know how to work with positive and negative numbers.

Not confident yet? Work through Quadratic equations first.

Worked example

One question from this skill's own question bank, shown with its full working.

Question

Solve: x + y = 10 and x − y = 4. Find x.

Answer: 7

Working: Add the equations: 2x = 14, so x = 7 (and y = 3).

Common mistakes to avoid

Mixing up addition and subtraction when eliminating a variable. Recheck the signs before you combine the equations.
Forgetting to change the inequality sign when multiplying by a negative number. Always watch the sign carefully.
Stopping after finding one variable and not finding the other. Use the value again to complete the pair.
Not checking whether the final values satisfy both equations or the inequality. Substitute them back to confirm.

Curriculum and exam alignment

Ghana GES SHS syllabusWASSCE

This work usually appears in SHS algebra lessons as part of equation solving and inequality practice. It supports the kind of reasoning often tested in WASSCE mathematics papers.

Curriculum notes are a general guide to where this work normally sits. Always check the syllabus your school or examination body is currently using.

Related skills

Other SHS Core: Algebra & Equations skills in Maths, at the same point in the course.

Quadratic equationsSHS

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Practise simultaneous equations & inequalities

6 questions with a worked answer after every attempt, and a SmartScore that tracks how close you are to mastery.

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