Taking into account the definition of a system of linear equations, the number of adults attended the Saturday matinee showing is 29 and the number of children attended the Saturday matinee showing is 16.
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 to say, 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:
The tickets to gone with the wind, at the classic movie house, cost $4.50 for adults and $2 for children.
45 people attended the Saturday matinee showing and the Classic movie House sold $162.50 worth of tickets.
So, the system of equations to be solved is
[tex]\left \{ {{x+y=45} \atop {4.50x+2y=162.5}} \right.[/tex]
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing 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 "x" from the first equation you get:
x=45 - y
Then, substituting the expression in the second equation you get:
4.50×(45 - y) +2y=162.5
Solving:
4.50×45 - 4.50y +2y=162.5
4.50×45 - 4.50y +2y=162.5
202.5 -2.5y= 162.5
-2.5y= 162.5 -202.5
-2.5y= -40
y= (-40)÷ (-2.5)
y=16
Now, replacing in the expression x=45 - y you get:
x=45 -y
x= 45-16
x= 29
Finally, the number of adults attended the Saturday matinee showing is 29 and the number of children attended the Saturday matinee showing is 16.
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