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.

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)

This solution is incorrect.

Explanation:

We will use the substitution method to solve this equation.

Then:

x - y = 75

x = 75 + y

x + y = 743

(75 + y) + y = 743

75 + 2y = 743

2y = 743 - 75

2y = 668

y = 668/2

y = 334

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.

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