SOLUTION: 2x-3y= 7 3x+7y= -1 answer (2,-1) need a break down of how my text book got the solutions 2, -1

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Question 186754: 2x-3y= 7
3x+7y= -1
answer (2,-1)


need a break down of how my text book got the solutions 2, -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%282x-3y=7%2C3x%2B7y=-1%29


3%282x-3y%29=3%287%29 Multiply the both sides of the first equation by 3.


6x-9y=21 Distribute and multiply.


-2%283x%2B7y%29=-2%28-1%29 Multiply the both sides of the second equation by -2.


-6x-14y=2 Distribute and multiply.


So we have the new system of equations:
system%286x-9y=21%2C-6x-14y=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:


%286x-9y%29%2B%28-6x-14y%29=%2821%29%2B%282%29


%286x%2B-6x%29%2B%28-9y%2B-14y%29=21%2B2 Group like terms.


0x%2B-23y=23 Combine like terms.


-23y=23 Simplify.


y=%2823%29%2F%28-23%29 Divide both sides by -23 to isolate y.


y=-1 Reduce.


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6x-9y=21 Now go back to the first equation.


6x-9%28-1%29=21 Plug in y=-1.


6x%2B9=21 Multiply.


6x=21-9 Subtract 9 from both sides.


6x=12 Combine like terms on the right side.


x=%2812%29%2F%286%29 Divide both sides by 6 to isolate x.


x=2 Reduce.


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


Which form the ordered pair .


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of 2x-3y=7 (red) and 3x%2B7y=-1 (green)