Question

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?

Answer 1

No

Explanation:

4A + 4O = 10

6A + 6O = 15

The second equation is just a multiple of the first one, so we don't have two distinct equations to solve for the prices

Answer 2

No

Explanation:

Say the price of 1 apple is x and the price of 1 orange is y. Then, we can write the two equations:

4x + 4y = 10

6x + 6y = 15

We can try to solve this by elimination, which means getting rid of one variable so that we're left with only 1 variable to solve for. Multiply the top equation by 3 and the bottom equation by 2:

3 * (4x + 4y) = 10 * 3 ⇒ 12x + 12y = 30

2 * (6x + 6y) = 15 * 2 ⇒ 12x + 12y = 30

Subtract the bottom equation from the top:

12x + 12y = 30

- 12x + 12y = 30

______________

0 + 0 = 0

Since we result in 0 = 0, that means any values of x and y we put into the equations will work, so we cannot find a unique price.

Hope this helps!