This study notes covers Worked Example 2: Substitution within Simultaneous Equations for GCSE Mathematics. Revise Simultaneous Equations in Algebra for GCSE Mathematics with 15 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 6 of 8 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Worked Example 2: Substitution

Solve: y = 2x + 1 and 3x + y = 11

Step 1 Substitute y into second equation

3x + (2x + 1) = 11

Step 2 Solve for x

5x + 1 = 11

5x = 10

x = 2

Step 3 Find y

y = 2(2) + 1 = 4 + 1 = 5

Step 4 Check

3(2) + 5 = 6 + 5 = 11 ✓

Practice questions for Simultaneous Equations

Which method is most efficient for solving the following simultaneous equations? 5x + 2y = 14 3x + 2y = 10

A. Substitution — rearrange the first equation for x, then substitute into the second.
B. Elimination — subtract the equations directly because the y-coefficients are already equal.
C. Elimination — multiply both equations by 5 and 3 respectively to match the x-coefficients.
D. Trial and improvement — test integer values of x and y until both equations are satisfied.

1 markfoundation

Ali solves the simultaneous equations 5x + y = 17 and x - y = 1 by elimination. Ben says he can also use substitution by rearranging x - y = 1 to get x = y + 1. Explain how elimination works for these two equations and state one advantage of Ben's substitution approach.

3 marksstandard

Quick recall flashcards

Steps for the elimination method

1. Match one set of coefficients (multiply if needed) 2. Same signs: subtract the equations 3. Different signs: add the equations 4. Solve for the remaining variable 5. Substitute back to find the other variable

What are simultaneous equations?

Two or more equations that share the same variables. Solving them finds the values of those variables that satisfy ALL equations at the same time.

Worked Example 1: Elimination

Common Mistakes to Avoid

Worked Example 2: Substitution

Worked Example 2: Substitution

Practice questions for Simultaneous Equations

Quick recall flashcards

15 questions on Simultaneous Equations — practise free