Ben went to the farmer’s market with $14.00, bought 2 pounds of cherries and still had enough money left to buy 3 pounds of appl
es. Tom went to the farmer’s market and bought 6 pounds of apples and 4 pounds of cherries for $28.00. 14 – 2y = 3x, 6x + 4y = 28
The boys solved the equations to find the price per pound that they paid for cherries and found the solution 14 = 14. How should they interpret this result?
A: The price of 4 pounds of cherries is $14.00.
B: The price of 2 pounds of cherries is $14.00.
C: They made a math error when solving the equations, and should try a different solution method to find the price of the cherries.
D: The two equations describe the same line, so there is not enough information to determine the price per pound of cherries.
Awould be the best answer here because equations with no solutions would be parallel. That means they would have the same slope but with different y-intercepts. Since where the equations share points would be the solution, they cannot share points either.