Pairs that make 10
If x + y = 10, then 2 and 8 work, and so do 4 and 6.
| x | y |
|---|---|
| 2 | 8 |
| 4 | 6 |
| 5 | 5 |
Both numbers together must match the total.
Year 6
Find pairs of numbers that satisfy an equation with two unknowns and enumerate possibilities of combinations of two variables
Find number pairs that make an equation true and list possibilities systematically.
Lesson overview
Algebra
When an equation has two unknowns, different pairs of values may satisfy it. We can test organised pairs and look for the rule that connects the two variables.
Stay systematic
Changing one value changes the other if the total must stay fixed.
A pattern helps you find all the possibilities.
Worked example
Find three pairs that satisfy a + b = 12.
| a | b |
|---|---|
| 1 | 11 |
| 4 | 8 |
| 6 | 6 |
- Choose a value for a.
- Subtract it from 12 to find b.
- Repeat with other values of a.
- Any pair that totals 12 satisfies the equation.
Try it
Choose one value, work out the matching value, then continue in an organised order.
Question 1
Which pair satisfies x + y = 10?
Question 2
Which pair satisfies a + b = 12?
Question 3
If p + q = 6 and p = 2, q =
| p | q |
|---|---|
| 2 | ? |
Question 4
Which list is organised systematically for x + y = 5?
Question 5
If m + n = 9, which pair does not work?
Common mistakes
Watch for these when working through the lesson.
- Testing pairs randomly and missing possibilities.
- Forgetting that both values must satisfy the whole equation.
- Stopping after finding only one correct pair when there are several.
Related topics
These ideas fit closely with this lesson.
- Express missing number problems algebraically.
- Generate and describe linear number sequences.