Me

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.

So here you're using system of equations. You can solve systems by graphing, elimination, or substitution. Ill use substitution. First lets solve for x. take the second equation and add y to both sides to get x by itself:
x - y = 75
x = y + 75 now plug y+75 in for x in the first equation
x + y = 743
(y +75) +y = 743 solve for y
2y +75 = 743 subtract 75
2y = 668 divide both sides by 2
y = 334
now plug this into any of the 2 equations to solve for x i chose the second one
x - y = 75
x - 334 = 75  add 334 to both sides
x = 409
This means x, sold before the tournament is 409 and y, sold at the door is 334. That means the assistant is wrong and accidentally flipped the two answers