Two apples and three bananas cost a total of £1.30. Seven apples and one banana cost a total of £1.70. Find the cost of a) one apple and b) one banana.

First, look at the key information from the question and form an equation for each of the first two sentences. These equations are as follows (let a represent the number of apples and b represent the number of bananas). Note that it is easier if you convert the prices to pence:
(1) 2a + 3b = 130
(2) 7a + b = 170
Next, you want to combine these equations in a way that eliminates either a or b. There are multiple ways of doing this. I would choose to first multiply (2) by 3 to form equation 3:
(3) 21a + 3b = 510
Then subtract (1) from (3) to form (4):
(4) 19a = 380
Solving (4) gives a = 20 (divide both sides by 19). If we rearrange (2) to make b the subject, then substitute a for 20, we get:
b = 170 - 7(20)
b = 170 - 140
b = 30
So the final answer is:
a) An apple costs 20p or £0.20b) A banana costs 30p or £0.30