SOLUTION: Solve each system of linear equation by an method. 3x + 4y = 1 2x + 3y = 1 Please help !

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Question 336671: Solve each system of linear equation by an method.
3x + 4y = 1
2x + 3y = 1
Please help !
Answer by jim_thompson5910(28593) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%283x%2B4y=1%2C2x%2B3y=1%29


3%283x%2B4y%29=3%281%29 Multiply the both sides of the first equation by 3.


9x%2B12y=3 Distribute and multiply.


-4%282x%2B3y%29=-4%281%29 Multiply the both sides of the second equation by -4.


-8x-12y=-4 Distribute and multiply.


So we have the new system of equations:
system%289x%2B12y=3%2C-8x-12y=-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:


%289x%2B12y%29%2B%28-8x-12y%29=%283%29%2B%28-4%29


%289x%2B-8x%29%2B%2812y%2B-12y%29=3%2B-4 Group like terms.


x%2B0y=-1 Combine like terms. Notice how the y terms cancel out.


x=-1 Simplify.


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9x%2B12y=3 Now go back to the first equation.


9%28-1%29%2B12y=3 Plug in x=-1.


-9%2B12y=3 Multiply.


12y=3%2B9 Add 9 to both sides.


12y=12 Combine like terms on the right side.


y=%2812%29%2F%2812%29 Divide both sides by 12 to isolate y.


y=1 Reduce.


So our answer is x=-1 and y=1.


Which form the ordered pair .


This means that the system is consistent and independent.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my website.

Jim