Solving Linear Equations
Linear equations are one of the most frequently tested algebra topics at Cambridge IGCSE level. Students must isolate the unknown variable by applying inverse operations, handling brackets and fractions along the way.
What You'll Learn
- Solving one-step and two-step equations
- Solving equations with unknowns on both sides
- Solving equations involving brackets
- Solving equations with fractional coefficients
Watch Out For These Mistakes
Students make these errors again and again. Knowing them in advance gives you a head start.
Performing an operation on one side of the equation without doing the same to the other
Making sign errors when moving terms across the equals sign
Forgetting to multiply every term inside the bracket when expanding before solving
What Examiners Say About Solving Linear Equations
Insights pulled from Cambridge IGCSE (0580) examiner reports — the exact mistakes candidates make every year.
- Misconception●●●●●
You can ONLY cancel FACTORS (things multiplied), not terms added/subtracted. Factorise numerator and denominator first, then cancel matching brackets. Never cancel x² from x² − 25.
Source: CIE 0580 · May/June 2021 · Paper 4 · Q7a
- Presentation●●●●●
In 'show that k = 8' questions, you must DERIVE 8, not assume it. Starting from 'k = 8' and working both ways is circular and scores zero. Work from the given info towards the target.
Source: CIE 0580 · May/June 2021 · Paper 3 · Q5
- Common Mistake●●●●●
When raising a power to a power, MULTIPLY the exponents: (x³)³ = x⁹, not x⁶. But for coefficients like (4x³)³, the coefficient is raised: 4³ = 64, not 4 × 3 = 12.
Source: CIE 0580 · Feb/March 2024 · Paper 2 · Q21b
Based on 3of 500+ insights extracted from CIE 0580 examiner reports (2018–2024).
Exam Coverage
This topic appears in the Cambridge IGCSE past papers. Our AI tutor can help with it on any question.
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Related Topics
Inequalities
Inequalities extend equation-solving skills by introducing ranges of solutions rather than single values. Students must solve, represent on number lines, and shade regions on graphs defined by multiple inequalities.
Rearranging Formulae
Rearranging formulae requires students to change the subject of an equation, using the same inverse-operation skills as solving equations but with multiple variables. Harder questions involve subjects that appear twice or under roots and powers.
Simultaneous Equations
Simultaneous equations require students to find values that satisfy two equations at the same time. Students solve pairs of linear equations, then go on to one linear and one quadratic equation together.
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