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

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) (Show Source): You can put this solution on YOUR website!
Start with the given system

Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute the negative

Combine like terms on the left side

Subtract 8 from both sides

Combine like terms on the right side

Divide both sides by -4 to isolate x

Divide

Now that we know that , we can plug this into to find

Substitute for each

Simplify

So our answer is and

Check:

Start with the first equation

Plug in and

works
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