Questions on Algebra: Systems of Linear Equations answered by real tutors!

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Question 153240: you have used all of a $50 gift certificate watching movies at the local theater. Afternoon movies are $4 and evening movies are $6. you have watched a total of 10 movies. HOw much have you spent on evening movies?: you have used all of a $50 gift certificate watching movies at the local theater. Afternoon movies are $4 and evening movies are $6. you have watched a total of 10 movies. HOw much have you spent on evening movies?
Answer by jim_thompson5910(9162) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=# of $6 movies and y=# of $4 movies

Since "you have watched a total of 10 movies", this means that the first equation is x+y=10

Also, since you only have $50 to spend, this means that the second equation is 6x+4y=50



So we have the system of equations:

system(x+y=10,6x+4y=50)


Let's use substitution to solve this system.

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.




So let's isolate y in the first equation

x+y=10 Start with the first equation


y=10-x Subtract x from both sides


y=-x+10 Rearrange the equation




---------------------

Since y=-x+10, we can now replace each y in the second equation with -x+10 to solve for x



6x+4highlight((-x+10))=50 Plug in y=-x+10 into the first equation. In other words, replace each y with -x+10. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



6x+(4)(-1)x+(4)(10)=50 Distribute 4 to -x+10


6x-4x+40=50 Multiply


2x+40=50 Combine like terms on the left side


2x=50-40Subtract 40 from both sides


2x=10 Combine like terms on the right side


x=(10)/(2) Divide both sides by 2 to isolate x



x=5 Divide





-----------------First Answer------------------------------


So the first part of our answer is: x=5









Since we know that x=5 we can plug it into the equation y=-x+10 (remember we previously solved for y in the first equation).



y=-x+10 Start with the equation where y was previously isolated.


y=-(5)+10 Plug in x=5


y=-5+10 Multiply


y=5 Combine like terms



-----------------Second Answer------------------------------


So the second part of our answer is: y=5









-----------------Summary------------------------------

So our answers are:

x=5 and y=5


This means that you bought 5 $6 movies and 5 $4 movies