SOLUTION: this is an elimination problem i can not get it. 3x+2y=3 9x-8y=-2

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Question 161680This question is from textbook intermediate algebra
: this is an elimination problem i can not get it.
3x+2y=3
9x-8y=-2 This question is from textbook intermediate algebra

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%2B2y=3%2C9x-8y=-2%29


4%283x%2B2y%29=4%283%29 Multiply the both sides of the first equation by 4.


12x%2B8y=12 Distribute and multiply.


So we have the new system of equations:
system%2812x%2B8y=12%2C9x-8y=-2%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:


%2812x%2B8y%29%2B%289x-8y%29=%2812%29%2B%28-2%29


%2812x%2B9x%29%2B%288y%2B-8y%29=12%2B-2 Group like terms.


21x%2B0y=10 Combine like terms. Notice how the y terms cancel out.


21x=10 Simplify.


x=%2810%29%2F%2821%29 Divide both sides by 21 to isolate x.


So the first part of the answer is x=%2810%29%2F%2821%29


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12x%2B8y=12 Now go back to the first equation.


12%2810%2F21%29%2B8y=12 Plug in x=10%2F21.


40%2F7%2B8y=12 Multiply.


7%2840%2Fcross%287%29%2B8y%29=7%2812%29 Multiply both sides by the LCD 7 to clear any fractions.


40%2B56y=84 Distribute and multiply.


56y=84-40 Subtract 40 from both sides.


56y=44 Combine like terms on the right side.


y=%2844%29%2F%2856%29 Divide both sides by 56 to isolate y.


y=11%2F14 Reduce.


So the second part of the answer is y=11%2F14


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Answer:


So the solutions are x=%2810%29%2F%2821%29 and y=11%2F14 which forms the ordered pair