SOLUTION: How do i write this into a linear system problem? " You go to the video store to rent 5 movies for the weekend: Movies rent for $2 and $3. You spend $13. How many $2 movies did

Question 137: How do i write this into a linear system problem?
" You go to the video store to rent 5 movies for the weekend: Movies rent for $2 and $3. You spend $13. How many $2 movies did you rent? How many $3 movies did you rent?
How do i write the two equations for that so i can solve it.
Answer by terrtwo(10) (Show Source): You can put this solution on YOUR website!
Linear equations assume that you have two equations to work with. In this case, there are two types of movies you can purchase that are different by price. Fi we designate one type movie as X and the other as Y, then we know the sum of these two variables must be 5;
--> x + y = 5 (equation #1)
For the second equation, we are told that a total of thirteen dollars is spent. This means that x movies cost 2 dollars each and y movies cost 3 dollars each;
--> 2x + 3y = 13 (equatin #2)
Once we have two valid equations, we can solve this easily using substitution. We solve equation one for x by subtracting y from both sides;
--> x + y - y = 5 - y
--> x = 5 - y
We then substitute (5 - y) for x in the second equation;
--> 2(5 - y) + 3y = 13
We distribute the 2;
--> 2*5 - 2*y + 3y = 13
--> 10 - 2y + 3y = 13
We combine like terms;
--> 10 + y = 13
We subtract 10 from both sides;
--> 10 + y - 10 = 13 - 10
--> y = 3
To now find x we got back and substitute 3 for y in the first equation;
--> x + 3 = 5
Substract 3 from both sides;
--> x + 3 - 3 = 5 - 3
--> x = 2
Hence we bought 2 of the two dollar movies and 3 of the three dollar movies.

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