SOLUTION: 2x+3y=4 x+4y=6

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Question 201434: 2x+3y=4
x+4y=6
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%282x%2B3y=4%2Cx%2B4y=6%29


-2%28x%2B4y%29=-2%286%29 Multiply the both sides of the second equation by -2.


-2x-8y=-12 Distribute and multiply.


So we have the new system of equations:
system%282x%2B3y=4%2C-2x-8y=-12%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:


%282x%2B3y%29%2B%28-2x-8y%29=%284%29%2B%28-12%29


%282x-2x%29%2B%283y-8y%29=4-12 Group like terms.


0x-5y=-8 Combine like terms.


-5y=-8 Simplify.


y=%28-8%29%2F%28-5%29 Divide both sides by -5 to isolate y.


y=8%2F5 Reduce.


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2x%2B3y=4 Now go back to the first equation.


2x%2B3%288%2F5%29=4 Plug in y=8%2F5.


2x%2B24%2F5=4 Multiply.


5%282x%2B24%2Fcross%285%29%29=5%284%29 Multiply both sides by the LCD 5 to clear any fractions.


10x%2B24=20 Distribute and multiply.


10x=20-24 Subtract 24 from both sides.


10x=-4 Combine like terms.


x=%28-4%29%2F%2810%29 Divide both sides by 10 to isolate x.


x=-2%2F5 Reduce.


So the solutions are x=-2%2F5 and y=8%2F5.


Which form the ordered pair .


This means that the system is consistent and independent.