SOLUTION: The difference of two numbers (the second minus the first) is 48. The second is 8 less than 5 times the first, What are the two numbers?

Question 122677: The difference of two numbers (the second minus the first) is 48. The second is 8 less than 5 times the first, What are the two numbers?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since "The difference of two numbers (the second minus the first) is 48", this means that the first equation is which then becomes

Also since "The second is 8 less than 5 times the first", the second equation is

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.

Combine like terms on the left side

Add 8 to 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 which also looks like

Notice if we graph the two equations, we can see that their intersection is at

. So this verifies our answer.

Graph of (red) and (green)

So the two numbers are

14 and 62
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