SOLUTION: I am working on this problem. I am trying to set it up correctly. The difference of two numbers is 48. The second is 8 less thatn 5 times the first. What are the two numbers. F

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Question 111841: I am working on this problem. I am trying to set it up correctly.
The difference of two numbers is 48. The second is 8 less thatn 5 times the first. What are the two numbers.
First I tried to set up the problem like this:
x-y=48
y=5x-8.
Since this is a subtraction problem I am not sure how to solve.
Could anyone please help me.
Thank you,
tracy
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system
x-y=48
y=5x-8



x-%285x-8%29=48 Plug in y=5x-8 into the first equation. In other words, replace each y with 5x-8. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


x-5x%2B8=48 Distribute the negative


-4x%2B8=48 Combine like terms on the left side


-4x=48-8Subtract 8 from both sides


-4x=40 Combine like terms on the right side


x=%2840%29%2F%28-4%29 Divide both sides by -4 to isolate x



x=-10 Divide




Now that we know that x=-10, we can plug this into y=5x-8 to find y



y=5%28-10%29-8 Substitute -10 for each x


y=-58 Simplify


So our answer is x=-10 and y=-58

Check:

x-y=48 Start with the first equation


-10-%28-58%29=48 Plug in x=-10 and y=-58


48=48 works