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?

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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) About Me  (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 y-x=48 which then becomes -x%2By=48


Also since "The second is 8 less than 5 times the first", the second equation is y=5x-8




Start with the given system
-x%2By=48
y=5x-8



-x%2B5x-8=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.



4x-8=48 Combine like terms on the left side


4x=48%2B8Add 8 to both sides


4x=56 Combine like terms on the right side


x=%2856%29%2F%284%29 Divide both sides by 4 to isolate x



x=14 Divide




Now that we know that x=14, we can plug this into y=5x-8 to find y



y=5%2814%29-8 Substitute 14 for each x


y=62 Simplify


So our answer is x=14 and y=62 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%28+500%2C+500%2C+-5%2C+35%2C+-5%2C+65%2C+48%2Bx%2C+5x-8%29+ Graph of -x%2By=48 (red) and y=5x-8 (green)






So the two numbers are


14 and 62