Free taster
5 of 6 sections open
Two Equations, Two Unknowns
Two Equations, Two Unknowns
If I tell you x + y = 10, can you find x and y? No! There are infinite possibilities (1+9, 2+8, 3+7...). But if I ALSO tell you x - y = 4, suddenly there's only ONE answer: x=7, y=3. Two equations with two unknowns can be solved - and the answer is where the two lines cross!
Visual: Two Methods for Solving
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.
Mathematics glossary
- 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.
Earn the mark scheme marks
Common Mistakes to Avoid
Wrong:
Subtracting when you should add (or vice versa)
Right:
Same signs → subtract. Different signs → add
Wrong:
Forgetting to multiply ALL terms when scaling
Right:
×3 means multiply EVERY term by 3 (both sides)
Wrong:
Not checking your answer
Right:
Always substitute back into BOTH equations
Now try it yourself
Quiz · Question 1 of 15
Which method is most efficient for solving the following simultaneous equations? 5x + 2y = 14 3x + 2y = 10
Tap an answer to check it
This topic in real past papers
Every real exam question we've found on simultaneous equations, with a full worked answer.