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) About Me  (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: system%28x%2B2y=5%2C2x%2By=4%29



Start with the given system of equations:
system%28x%2B2y=5%2C2x%2By=4%29


-2%28x%2B2y%29=-2%285%29 Multiply the both sides of the first equation by -2.


-2x-4y=-10 Distribute and multiply.


So we have the new system of equations:
system%28-2x-4y=-10%2C2x%2By=4%29


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


%28-2x-4y%29%2B%282x%2By%29=%28-10%29%2B%284%29


%28-2x%2B2x%29%2B%28-4y%2B1y%29=-10%2B4 Group like terms.


0x%2B-3y=-6 Combine like terms.


-3y=-6 Simplify.


y=%28-6%29%2F%28-3%29 Divide both sides by -3 to isolate y.


y=2 Reduce.


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-2x-4y=-10 Now go back to the first equation.


-2x-4%282%29=-10 Plug in y=2.


-2x-8=-10 Multiply.


-2x=-10%2B8 Add 8 to both sides.


-2x=-2 Combine like terms on the right side.


x=%28-2%29%2F%28-2%29 Divide both sides by -2 to isolate x.


x=1 Reduce.


So the solutions are x=1 and y=2.


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