# Simultaneous equations

Two equations with two unknowns that are both true at once. You find the pair of values that fits both.

Maths (school) · Part 03: Equations and formulae · Card 5 of 8 · Last updated 2026-10-19

## Analogy

Like finding the one meeting point of two roads on a map.

## Example

**2x + y = 11
x + y = 7**

Subtract: x = 4
Put x = 4 in x + y = 7: y = 3
Check: 8 + 3 = 11

## In practice

If 2 coffees and 1 tea cost 11 pounds and 1 coffee and 1 tea cost 7 pounds, you can find each price.

## Practice

### Flashcards

- **Solve 2x + y = 11 and x + y = 7.** x = 4 and y = 3. Subtract the equations to remove y.

### Interview questions

**Solve the simultaneous equations 2x + y = 11 and x + y = 7, and explain your method.**

- Subtract to remove y
- This gives x = 4
- Substitute into x + y = 7 to get y = 3
- Check in both equations

## Questions people ask

### What is the elimination method?

You add or subtract the two equations so that one letter disappears. In 2x + y = 11 and x + y = 7, subtracting removes y and leaves x = 4. Then put that value back into either equation to find the other letter.

### How do you know the answers are correct?

Put both values into both original equations. If both come out true, the answer is right. For x = 4 and y = 3, the first gives 8 + 3 = 11 and the second gives 4 + 3 = 7. Both match.

## Related concepts

- [Solving linear equations](https://studyvisually.com/learn/science/maths-school/maths-school-part-3/maths-school-part-3-concept-1)
- [Unknowns on both sides](https://studyvisually.com/learn/science/maths-school/maths-school-part-3/maths-school-part-3-concept-2)
- [Changing the subject](https://studyvisually.com/learn/science/maths-school/maths-school-part-3/maths-school-part-3-concept-3)
- [Inequalities](https://studyvisually.com/learn/science/maths-school/maths-school-part-3/maths-school-part-3-concept-4)

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