Let's define the next variables:
x: price of one apple
y: price of one banana
Patricia bought 4 apples and 9 bananas for $12.70, means:
4x + 9y = 12.70 (eq. 1)
Jose bought 8 apples and 11 bananas for $17.70, means:
8x + 11y = 17.70 (eq. 2)
Multiplying equation 1 by 2, we get:
2(4x + 9y) = 2*12.70
2*4x + 2*9y = 25.4
8x + 18y = 25.4 (eq. 3)
Subtracting equation 2 to equation 3, we get:
8x + 18y = 25.4
-
8x + 11y = 17.70
-------------------------
7y = 7.7
y = 7.7/7
y = 1.1
Replacing this result into equation 1 and solving for x, we get:
4x + 9*1.1 = 12.70
4x + 9.9 = 12.70
4x = 12.70 - 9.9
4x = 2.8
x = 2.8/4
x = 0.7
The price of one apple is $0.70