Part 03 · Equations and formulae · Card 5 of 8
Simultaneous equations
Two equations with two unknowns that are both true at once. You find the pair of values that fits both.
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Analogy
Like finding the one meeting point of two roads on a map.
Example
2x + y = 11
x + y = 7
Subtract: x = 4Put x = 4 in x + y = 7: y = 3Check: 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.