A fruit stand has to decide what to charge for their produce. They decide to charge $5.30 for 1 apple and 1 orange. They also plan to charge $14 for 2 apples and 2 oranges. We put this information into a system of linear equations. Can we find a unique price for an apple and an orange?

No, we cannot.

Step-by-step explanation:

Let a represent the number of apples and r represent the number of oranges.

The first equation would then be

1a + 1r = 5.30

The second equation would be

2a + 2r = 14

We can see that the coefficients in the second equation are double those in the first equation. However, if we multiply the first equation by 2, we get

2 (1a + 1r = 5.30) → 2a + 2r = 10.60

The constant at the end of the equation is not 14, but the coefficients of the variables are the same. This means this describes a line parallel to this line; this means they will not intersect and thus there is no solution to this system.

can not find a unique price for an apple and an orange.