Taking into account the definition of a system of linear equations, the amount of student tickets sold is 140 and the amount of non-student tickets sold is 420.
A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
In this case, a system of linear equations must be proposed taking into account that:
On one side, there were 560 tickets sold for a basketball game. This is represented by x+y= 560
On the other side, the price of a student ticket is $5.25 and a non-student ticket costs $8.75. If $4410 was collected, the equation that represents this situation is 5.25x + 8.75y= 4410
So, the system of equations to solve is:
[tex]\left \{ {{x+y=560} \atop {5.25x + 8.75y= 4410}} \right.[/tex]
There are various methods to solve a system of equations, it is decided to solve by the substitution method, which consists of solving one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable "y" from the first equation, you obtain:
y = 560 -x
Replacing in the second equation you get the expression:
5.25x + 8.75(560 -x)= 4410
Solving:
5.25x + 8.75×560 -8.75x= 4410
5.25x + 4900 -8.75x= 4410
5.25x -8.75x= 4410 -4900
-3.5x= -490
x= (-490)÷(-3.5)
x=140
Finally, to obtain the value of y, it is replaced in the expression previously obtained for y:
y=560 - x
y=560 - 140
y= 420
Finally, remembering that x represents the amount of student tickets sold and y represents the amount of non-student tickets sold, then the amount of student tickets sold is 140 and the amount of non-student tickets sold is 420.
Learn more about system of linear equations:
