Question

Coach Johnson knows that this system of equations represents the number of tickets sold before the tournament, x, and at the door, y.
x + y = 743
x – y = 75
An assistant told him that 409 tickets were sold at the door and 334 tickets were sold before the tournament. Is this solution correct? Explain.

Answer 1

Answer:

This solution is incorrect.

Explanation:

We will use the substitution method to solve this equation.

• The first step is to isolate one of the unknowns to find the solution, in which case we will isolate the x.

Then:

x - y = 75

x = 75 + y

• In the second step, we will replace the x found in the second equation to solve the first equation.

x + y = 743

(75 + y) + y = 743

75 + 2y = 743

2y = 743 - 75

2y = 668

y = 668/2

y = 334

• In the third step, we substitute the value of y in any of the questions to find the final result:

x - y = 75

x - 334 = 75

x = 75 + 334

x = 409

Therefore, if x represents the number of tickets sold before the tournament, and y represents the number of tickets sold at the door, and as the values of x = 409 and y = 334, we can conclude that the assistant made a mistake and inverted the values.

Answer 2

Answer:

Sample Response: No, the assistant’s solution is incorrect. The solution (334, 409) satisfies the first equation, but not the second. The assistant mixed up the numbers. The solution should be (409, 334)

Explanation:hope this helps