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

Linear Equations

• Let the price of an apple be $x and that of an orange be $y.

• Condition 1.
• They need $10 for 4 apples and 4 oranges.
• Then, 4x + 4y = 10
• or, 2x + 2y = 5 .....(1)

• Condition 2.
• They needs $15 for 6 apples and 6 oranges.
• Then, 6x + 6y = 15
• or, 2x + 2y = 5 .....(2)

• We have found two identical linear equations.
• However they form a dependent system of linear equations, which reduces to:
• 2x + 2y = 5

• This linear equation has infinite number of solutions.
• Thus we conclude that we cannot find a unique price for an apple and an orange.

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Answer 2

Answer:

No; the system has many solutions.

Step-by-step explanation: