Name both unknowns before writing anything. Two unknowns need two equations.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
One equation per condition
A total count gives one equation; a total cost gives another.
Then solve
Substitution or elimination — whichever the numbers make easier.
Answer the question asked
The algebra gives numbers; the question asked about tickets or coins.
Two unknowns need two equations
A situation with two unknown quantities needs two independent pieces of information. Identify both, define a letter for each, and write one equation per piece. Missing one leaves the system unsolvable.
The standard situations
Two plans that cost the same; a mixture of two things with a known total and a known value; two rates working together. Recognising the type usually tells you what the two equations will look like.
Keep the units consistent
One equation often counts items and the other counts value or weight. Mixing the two — adding a count to a cost — produces an equation that solves cleanly and means nothing. Label each equation with what it counts.
Interpret and sanity-check
A solution of x = −3 tickets or x = 2.5 people signals a modelling error, not just an arithmetic one. Checking the answer against the situation is as necessary as checking it against the equations.
Step 2: Try It Yourself
Tap and try it out.
adult and child
6
9
all tickets
?
The hatched bar is the piece the story is asking for.
Step 3: Watch an Example
One step at a time.
Watch Priya Set Up Two Equations
15 tickets sold. Adults cost £8, children £5, and the total was £96.
- Step 1
She names them: a adults and c children.
Step 4: Your Turn
Practice makes it stick.
The Count
Problem 1 of 2
a + c = 15 and a = 7. What is c?
The Money
Problem 2 of 2
7 adults at £8 each. How much, in pounds?
Two Conditions
1 of 8
x + y = 10 and x − y = 4. What is x?
2 of 8
Same system. What is y?
3 of 8
How many equations are needed for two unknowns?
4 of 8
2x + y = 12 and y = 4. What is x?
5 of 8
20 coins are 5p and 10p, worth 150p. If there are 10 tens, how many fives?
6 of 8
Order the steps for a system word problem.
- 1Write one equation per condition
- 2Solve the system
- 3Answer in the words of the problem
- 4Name both unknowns
7 of 8
x + y = 9 and x = 2y. What is y?
8 of 8
Same system. What is x?
Step 5: Quick Check
Show what you know.
Question 1 of 1
x + y = 12 and x − y = 2. What is x?
What You Learned
- Two unknowns need two independent conditions.
- Each condition in the story becomes one equation.
- Finish by answering in the words of the problem, not as bare numbers.