Taking into account the definition of a system of linear equations, the system of equations that could be used to determine the number of games Kadeesha played and the number of rides Kadeesha went on is:
[tex]\left \{ {{2.50G+4.75R=48.75} \atop {G=2R}} \right.[/tex]
where G is the number of games Kadeesha played and R is the number of rides Kadeesha went on.
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 give the solution proposed in both equations.
In this case, a system of linear equations must be proposed taking into account that:
On the other hand, you know:
So, the system of equations to be solved is
[tex]\left \{ {{2.50G+4.75R=48.75} \atop {G=2R}} \right.[/tex]
Among the different existing methods to solve the system of equations, it is decided to solve it using the substitution method. This method 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, substituting the second equation in the first one you get:
2.50×2R+4.75R=48.75
Solving:
5R+4.75R=48.75
9.75R=48.75
R= 48.75÷ 9.75
R= 5
Remembering that G=2R, you obtain that G=2×5= 10
In summary, the system of equations that could be used to determine the number of games Kadeesha played and the number of rides Kadeesha went on is:
[tex]\left \{ {{2.50G+4.75R=48.75} \atop {G=2R}} \right.[/tex]
where G is the number of games Kadeesha played and R is the number of rides Kadeesha went on.
Finally, the number of games played is 10 while the number of rides she went on is 5.
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