A fruit stand has to decide what to charge for their produce. They need $10 for 4 apples and 4 oranges. They also need $15 for 6 apples and 6 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 find a unique price for an apple and an orange.

Step-by-step explanation:

Let the price of an apple = x and the price of an orange = y (in dollars)

As, we have that,

They charge $10 for 4 apples and 4 oranges and $15 for 6 apples and 6 oranges.

So, we have the system of equations as,

4x + 4y = 10 ... (1)

6x + 6y = 15 ... (2)

Multiply equation (1) by 6 and equation (2) by 4, we get the equations,

24x + 24y = 60

24x + 24y = 60

As, both the equations are same, so they are dependent on each other.

Thus, there can be infinitely many solutions of this system of equations.

Hence, we cannot find a unique price for an apple and an orange.