SOLUTION: The sum of two numbers is 76. The second is 8 more than 3 times the first. What are the two numbers?

Question 122885: The sum of two numbers is 76. The second is 8 more than 3 times the first. What are the two numbers?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If "The sum of two numbers is 76", then the first equation is

Also, if "The second is 8 more than 3 times the first", then the second equation is

So we have the 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

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 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)

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