Home → Curriculum Hub → Maths Lessons → Schemes of Work → Three-Year GCSE Foundation → Simultaneous Equations
This Foundation GCSE scheme of work unit covers simultaneous equations in Year 11. It is about two equations that are true at the same time. Students read the intersection of two straight lines, solve by substitution, then by elimination, and finish by forming a pair from a worded problem.
Students have to find a pair of values, not a single x, and they have to check that pair in both original equations. That check is what later linear-quadratic pairs on Higher, and Foundation worded items, both need.
A student who has secured this unit:
Students should be secure with the following before beginning this unit.
Two unknowns need two equations. The solution is the pair (x, y) that sits on both lines, not an x on its own.
If one equation already gives y in terms of x, substitute that expression into the other. Then solve the one- unknown equation that remains.
Scale one or both equations so that a pair of coefficients matches. Add to cancel opposite signs; subtract to cancel matching signs.
A worded problem becomes two sentences, then two equations. The letters must stay the same from the sentences to the check.
| Misconception | Teaching focus |
|---|---|
| Finding x and then stopping, so y is never calculated. | Write the answer line as (x, y) = before any solving starts. |
| Adding when the matching coefficients have the same sign, so the unknown doubles instead of vanishing. | Ask same sign or opposite sign before the pair is combined. |
| Subtracting misaligned terms, so an x is taken from a y. | Draw a vertical line through the x column and through the y column. |
| Trying to eliminate before the coefficients are equal in size. | Scale the first equation so the chosen coefficients match, then combine. |
| Skipping the check in the second equation, so an arithmetic slip survives. | Substitute the pair into both originals and tick each one. |
Every lesson in this unit is already built. A Mr Mathematics membership gives you the presentation, worksheet, question generator and video tutorial for all 4 lessons, alongside the full Key Stage 3, GCSE, IGCSE and A-Level libraries.
A school membership covers every teacher in your department, so the whole scheme of work is resourced from one subscription.
Students learn how to graphically solve a pair of simultaneous equations.
Later, as learning progresses, they solve equations in the form y = mx + c and ax + by = c.
Students learn to solve a pair of simultaneous equations using the substitution method.
Later, as learning progresses, they set up and solve a pair of simultaneous equations to model real-life problems.
Students learn to solve a pair of simultaneous equations using the elimination method.
Later, they solve equations with different coefficients as learning progresses.
Students learn how to set up and solve a pair of simultaneous equations.
Later, they use simultaneous equations to model real-life problems as learning progresses.
Students gain additional practice solving simultaneous equations through elimination.
The problem solving activity challenges to set up and solve a pair of simultaneous equations to find an area.
Solving Simultaneous Equations Through Elimination
Students are challenged to set up and solve pairs of simultaneous equations to model real-life situations.
Five problems link to indices, volume, angles, perimeter and straight-line graphs.
Solving Simultaneous Equations Through Elimination
Solving Problems with Simultaneous Equations
Students revise how to solve a pair of simultaneous equations by elimination.
Later, as learning progresses set up a pair of simultaneous equations to solve complex, real-life problems.
Solving Simultaneous Equations Through Elimination
Solving Problems with Simultaneous Equations
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