Coach Johnson knows that this system of equations represents the number of tickets sold before the tournament, x, and at the doo
r, 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.
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.
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)
