Chapters
Solving Simultaneous Equations Using Substitution (Class 10 Guide)
Simultaneous equations are pairs (or sometimes sets) of equations that must be true at the same time. In GCSE Maths, you’ll often meet them in the form of two equations with two unknowns (usually x and y). For example:
The substitution method is one of the main ways to solve these equations. It works by replacing one variable with an equivalent expression from the other equation — so you reduce the problem to a single equation with just one unknown.
Step-by-step method
1. Make one variable the subject
Looking back at the equations above, pick one that is already written (or can easily be rearranged) to express x or y in terms of the other. For example:
2. Substitute into the other equation
Replace the y in the second equation with the expression 2x+1. So:
3. Simplify and solve
Now you only have one variable:
4. Substitute back
Put this value of x into the expression for y:
5. Write the solution as a pair
The solution to the simultaneous equations is:
Practice Questions & Solutions
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nice work
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