In this activity, we will look at equations with two unknowns.

a and b stand for two numbers, which could be different or the same.

Look at this equation.

a + 2b = 8

It tells you that a added to double b is 8

If a is 6, then b will be 1 because 6 + 2 × 1 = 6 + 2 = 8

If a = 2, then b = 3 because 2 + 2 × 3 = 2 + 6 = 8

If a = 1, then b = 3½ because 1 + 2 × 3½ = 1 + 7 = 8

Example

3a - 2b = 7

Which of these solutions satisfy the equation?

a = 7, b = 0

a = 7, b = 7

a = 4, b = 2½

a = 5, b = 3

Answer

Put the given pairs into the equation to see if 3a - 2b is 7 or not.

In each case, we work out 3 × a take away 2 × b to see if the answer is 7 or not.