Answer:
We can't find a unique price for an apple and an orange.
Step-by-step explanation:
Suppose, the price of an apple is [tex]x[/tex] and the price of an orange is [tex]y[/tex]
They need $10 for 4 apples and 4 oranges. So, the first equation will be.......
[tex]4x+4y=10 ........................................(1)[/tex]
They also need $15 for 6 apples and 6 oranges. So, the second equation will be........
[tex]6x+6y= 15 ........................................(2)[/tex]
Dividing equation (1) by 2 on both sides : [tex]2x+2y= 5[/tex]
Dividing equation (2) by 3 on both sides : [tex]2x+2y=5[/tex]
So, we can see that both equation (1) and (2) are actually same. That means, we will not get any unique solution for [tex]x[/tex] and [tex]y[/tex] here. Both [tex]x[/tex] and [tex]y[/tex] have "infinitely many solutions".
Thus, we can't find a unique price for an apple and an orange.
