Simultaneous equations are a key part of the GCSE Maths curriculum across AQA, Edexcel, and OCR. These problems often involve real-world scenarios like finance, distance-time problems, or comparing costs. Understanding how to set up and solve simultaneous equations using substitution or elimination methods can help you tackle context-based questions with confidence.

Strengthen your GCSE equation-solving skills

🔹 What Are Simultaneous Equations?

Simultaneous equations involve two or more equations that share variables. The solution is the values of the variables that satisfy all equations at once. In GCSE exams, they’re often presented within practical, real-life problems.

✅ Example:

Solve these using substitution or elimination to find the values of x and y.

🔸 How to Solve Simultaneous Equations

1. Elimination Method

Eliminate one variable by adding or subtracting the equations.

2. Substitution Method

Rearrange one equation to express one variable in terms of the other, then substitute.

📌 Example Using Substitution:

Substitute Equation 1 into Equation 2:

Then:   y = 12-5 = 7

🔸 Real-World Contexts in GCSE Exams

Simultaneous equations can model many real-life situations:

🧮 Cost Problems:

“Two pens and three pencils cost £2.10. Four pens and two pencils cost £3.40. What is the price of each item?”

Let x = cost of a pen, y = cost of a pencil:

🚗 Distance-Time Problems:

“A car and a bike travel a combined distance of 90 km in 2 hours. The car travels 60 km/h faster than the bike.”

Let x = speed of bike, y = speed of car. Use distance = speed * time to build equations.

🧠 Exam Tips for Simultaneous Equations

• Read the question carefully and define variables clearly
• Use correct units (e.g., £, km/h, hours)
• Choose elimination when the coefficients align easily
• Use substitution when one variable is already isolated
• Check your answers in both original equations

📝 Practice Questions

1. Three apples and two bananas cost £1.60. Two apples and four bananas cost £1.80. Find the price of each.
2. A train and a coach travel a total of 240 miles. The train travels 40 miles more than the coach. The coach speed is 60 mph and the journey takes 2 hours. Find the speed of the train.
3. Two numbers add to 20. Twice one number minus the other is 10. Find the numbers.
4. A student spends £15 on 5 pens and 3 notebooks. Another student spends £12 on 3 pens and 3 notebooks. Find the price of a pen and a notebook.

✅ Final Thoughts

Context-based simultaneous equation problems test not just your maths skills, but also your ability to apply logical thinking to real-life scenarios. With consistent practice and the right approach—choosing the best method, structuring equations properly, and interpreting word problems—you can tackle these questions confidently in any GCSE exam.

For in-depth tutorials, exam-style worksheets, and personalised help, visit GCSE Maths Tutor and take your equation-solving skills to the next level.