SOLUTION: A first number plus twice a second number is 5. Twice the first number plus the second totals 4. Find the numbers.

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Question 197997: A first number plus twice a second number is 5. Twice the first number plus the second totals 4. Find the numbers.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
"A first number plus twice a second number is 5. Twice the first number plus the second totals 4" translates to the system:



Start with the given system of equations:



Multiply the both sides of the first equation by -2.


Distribute and multiply.


So we have the new system of equations:



Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:





Group like terms.


Combine like terms.


Simplify.


Divide both sides by to isolate .


Reduce.


------------------------------------------------------------------


Now go back to the first equation.


Plug in .


Multiply.


Add to both sides.


Combine like terms on the right side.


Divide both sides by to isolate .


Reduce.


So the solutions are and .


which means that the first number is 1 and the second number is 2

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