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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