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?
Answers
Answered by
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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:
No; the system has many solutions.
Step-by-step explanation:
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