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Twice one number added to another number is 18. Four times the first number minus the other number is 12. Find the numbers.

Guest May 26, 2017
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Number 1:5

Number 2:8

 

In this problem, "one number" and "another number" are simply referring to variables like x and y. "Is" means equal to. Therefore, twice one number is simply 2 multiplied by a variable. For my variables, I'll simply use x and y.

 

\(2x+y=18\)

\(4x-y=12\)

 

This is a system of equations. Normally, I gravitate toward substitution, but I'll actually use elimination to solve this. Notice how there is a y-term and a negative y-term. I can add the equations together to get this:

 

\(6x=30\)

 

Divide by 6 on both sides:

 

\(x=5\)

 

Okay, our first number is equal to five. To find the next number, y, substitute 5 into one of the equations. It doesn't matter which one; you'll get the same answer:

 

\(2(5)+y=18\)

 

Simplify 2*5:

\(10+y=18\)

 

Subtract 10 on both sides to isolate y, our second number:

\(y=8\)

TheXSquaredFactor  May 26, 2017

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