SOLUTION: need help to solve this please 3x+4y=5, 2x+y=1

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Question 591322: need help to solve this please
3x+4y=5,
2x+y=1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%283x%2B4y=5%2C2x%2By=1%29


-4%282x%2By%29=-4%281%29 Multiply the both sides of the second equation by -4.


-8x-4y=-4 Distribute and multiply.


So we have the new system of equations:
system%283x%2B4y=5%2C-8x-4y=-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:


%283x%2B4y%29%2B%28-8x-4y%29=%285%29%2B%28-4%29


%283x%2B-8x%29%2B%284y%2B-4y%29=5%2B-4 Group like terms.


-5x%2B0y=1 Combine like terms.


-5x=1 Simplify.


x=%281%29%2F%28-5%29 Divide both sides by -5 to isolate x.


x=-1%2F5 Reduce.


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3x%2B4y=5 Now go back to the first equation.


3%28-1%2F5%29%2B4y=5 Plug in x=-1%2F5.


-3%2F5%2B4y=5 Multiply.


5%28-3%2Fcross%285%29%2B4y%29=5%285%29 Multiply both sides by the LCD 5 to clear any fractions.


-3%2B20y=25 Distribute and multiply.


20y=25%2B3 Add 3 to both sides.


20y=28 Combine like terms on the right side.


y=%2828%29%2F%2820%29 Divide both sides by 20 to isolate y.


y=7%2F5 Reduce.


So the solutions are x=-1%2F5 and y=7%2F5.


Which form the ordered pair .


This means that the system is consistent and independent.