Paper 1 · Algebra
⏱ Tested in 5 exam questions since 2022
Lesson 19 of 23
Algebra 19 – Simultaneous Equations by substitution
In this lesson you’ll learn to
- Spot when a squared term forces the substitution method over elimination
- Isolate a variable in the linear equation and substitute into the quadratic
- Solve the resulting quadratic and back-substitute for both solution pairs
- Present paired answers as coordinates (x, y)
Formula used
Roots of the quadratic equation
x = (-b ± √(b² − 4ac)) / 2a
On page 20 of the log tables — read it off, don’t memorise.Most recent exam questions
- 2025 Paper 1 Q4(a) — simultaneous equations — one linear, one quadratic. The linear equation gives y; substit…
- 2025 Paper 1 Q5(c) — simultaneous equations (one linear + one non-linear), plus the geometric insight "on the…
- 2024 Paper 1 Q1(c) — non-linear simultaneous equations — one quadratic equation in x, y and one linear equati…
- 2022 Paper 1 Q4(a) — simultaneous equations — line and a (non-linear) curve
- 2022 Paper 2 Q1(c) — translate two probability conditions into two simultaneous linear equations
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