Question 153240
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=50-40}}}Subtract 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