Year 6 Exam > Year 6 Notes > Year 6 Mathematics > Find pairs of values that satisfy equations with two variables
Find pairs of values that satisfy equations with two variables | Year 6 Mathematics PDF Download
What are variables?
- In mathematics, it's common to use letters to represent numbers.
- These letters, known as variables, can change their values according to specific rules or conditions given in the problem.
Examples
Example 1: Jasmine has some 20p and 50p coins.
Altogether she has £2.40
How many of each coin could she have?
Sol: Jasmine decides to displays her answers in a table:
The table allows her to be able to check that she has all the possible answers!
Can you explain each line of the table? What does the ‘x’ represent?
This is another example of a problem with two unknowns – how many 50p coins and how many 20p coins to have a given total.
Clearly there is not an infinite number of solutions
In fact there are just two possible solutions:
(2 x 50p) + (7 x 20p)
and
(4 x 50p) + (2 x 20p)
Example 2: What is the value of A?
What number do we have to add to 7 to make 12?
What is the value of the unknown to make both sides of this equation balance?
Sol: a + 7 = 12
There is only one answer to the value of the letter a. No other values of a will make the equation balance!
To find a, you can subtract 7 from 12.
12 - 7 = 5
The answer is: a = 5
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