Simultaneous Equations: Full GCSE Maths Lesson

A complete, ready to teach GCSE maths lesson on simultaneous equations: elimination, substitution and graphs, with worked answers on every slide. 29 slides, with teacher notes on every slide.

The lesson builds step by step from the idea that one pair of values makes both equations true, shown on a graph where two lines cross, through to solving harder pairs and real life problems. It covers:

• Learning objectives at three levels: must, should and could
• A warm up on the skills students need, with answers
• Key words: simultaneous, coefficient and eliminate
• The elimination method in five clear steps, with the rule “same signs subtract, different signs add”
• Worked examples: subtracting, adding and multiplying one equation to match coefficients
• Your turn questions with a full answer slide
• Harder pairs: multiplying both equations, solving by substitution, and a line and curve pair such as y = x² and y = x + 6 (Higher tier)
• A practice set of six pairs with answers
• Problem solving: cinema ticket prices and a café order
• An exam style question (5 marks) with an M1, A1, C1 mark scheme
• Common mistakes, an exit ticket with answers and a key points summary

Every worked example is set out one step at a time, and a consistent colour code highlights the coefficients being matched and the letter being eliminated, so students can follow the method easily. All diagrams are editable PowerPoint shapes.

Suitable for Year 10 and Year 11, GCSE Foundation and Higher tier, and matches AQA, Edexcel and OCR specifications.

If you find this lesson useful, please leave a review. It is part of a growing series of premium GCSE maths lessons, including Solving Linear Equations, Expanding and Factorising Quadratics, Pythagoras’ Theorem, Trigonometry (SOHCAHTOA) and Area and Circumference of Circles.