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

Subtracting Eqn 1 from Eqn 3

Dividing both sides by 18

Putting y=5.50 in Eqn 2

Dividing both sides by 3

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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Parallel lines have same slope, so first isolate y to get the equation into y=mx+b form.
-2x+3y=2
3y = 2x + 2

Now plug the point (3,4) into y = 2x + b
4 = 2(3) + b
Solves for be
b = -2
So the new equation is y = 2x - 2
-79, -55, 18, 44, 101, 143