The rent for one movie is $4.50 and rent for one video game is $5.50
Step-by-step explanation:
Let,
Rent for one movie = x
Rent for one video game = y
According to given statement;
12x+2y=65 Eqn 1
3x+5y=41 Eqn 2
Multiplying Eqn 2 by 4
[tex]4(3x+5y=41)\\12x+20y=164\ \ \ \ Eqn\ 3[/tex]
Subtracting Eqn 1 from Eqn 3
[tex](12x+20y)-(12x+2y)=164-65\\12x+20y-12x-2y=99\\18y=99\\[/tex]
Dividing both sides by 18
[tex]\frac{18y}{18}=\frac{99}{18}\\y=5.50[/tex]
Putting y=5.50 in Eqn 2
[tex]3x+5(5.50)=41\\3x+27.50=41\\3x=41-27.50\\3x=13.50[/tex]
Dividing both sides by 3
[tex]\frac{3x}{3}=\frac{13.50}{3}\\x=4.50[/tex]
The rent for one movie is $4.50 and rent for one video game is $5.50
Keywords: linear equation, elimination method
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