SOLUTION: 3x-2y=12 x+2y=6

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Question 179039This question is from textbook glencoe mathematics
: 3x-2y=12
x+2y=6 This question is from textbook glencoe mathematics

Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
3x-2y=12
x+2y=6
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Add to solve for "x":
4x = 18
x = 9/2
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Substitute to solve for "y":
(9/2) + 2y = 6
2y = 3/2
y = 3/4
==============
Cheers,
Stan H.

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-2y=12%2Cx%2B2y=6%29


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


%283x-2y%29%2B%28x%2B2y%29=%2812%29%2B%286%29


%283x%2Bx%29%2B%28-2y%2B2y%29=12%2B6 Group like terms.


4x%2B0y=18 Combine like terms.


4x=18 Simplify.


x=%2818%29%2F%284%29 Divide both sides by 4 to isolate x.


x=9%2F2 Reduce.


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3x-2y=12 Now go back to the first equation.


3%289%2F2%29-2y=12 Plug in x=9%2F2.


27%2F2-2y=12 Multiply.


2%2827%2Fcross%282%29%29-2%282y%29=2%2812%29 Multiply EVERY term by the LCD 2 to clear any fractions.


27-4y=24 Multiply.


-4y=24-27 Subtract 27 from both sides.


-4y=-3 Combine like terms on the right side.


y=%28-3%29%2F%28-4%29 Divide both sides by -4 to isolate y.


y=3%2F4 Reduce.

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Answer:


So the solutions are x=9%2F2 and y=3%2F4.


Which form the ordered pair .


This means that the system is consistent and independent.