Many real problems have two unknowns linked by two facts. You can write one equation for each fact and solve the system.
A worked example
"The sum of two numbers is 11 and their difference is 3. Find the numbers."
Let the larger number be x and the smaller be y. The two facts give:
x + y = 11
x − y = 3
Add the equations: 2x = 14, so x = 7. Then y = 11 − 7 = 4. The numbers are 7 and 4.
How to set one up
- Name each unknown with a letter.
- Turn each sentence or fact into one equation.
- Solve by substitution or elimination, then check the answer makes sense in the story.
Three rules that always help
- One unknown per letter, one equation per fact.
- Two unknowns usually need two equations.
- Check the answer against the words, not just the algebra.
Keep going
- Practice: Systems from word problems
- Back to the systems overview