SOLUTION: How do you solve -3x+y=7 5x+2y=3

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Question 560785: How do you solve -3x+y=7
5x+2y=3
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%28-3x%2By=7%2C5x%2B2y=3%29


-2%28-3x%2By%29=-2%287%29 Multiply the both sides of the first equation by -2.


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


So we have the new system of equations:
system%286x-2y=-14%2C5x%2B2y=3%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-2y%29%2B%285x%2B2y%29=%28-14%29%2B%283%29


%286x%2B5x%29%2B%28-2y%2B2y%29=-14%2B3 Group like terms.


11x%2B0y=-11 Combine like terms.


11x=-11 Simplify.


x=%28-11%29%2F%2811%29 Divide both sides by 11 to isolate x.


x=-1 Reduce.


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6x-2y=-14 Now go back to the first equation.


6%28-1%29-2y=-14 Plug in x=-1.


-6-2y=-14 Multiply.


-2y=-14%2B6 Add 6 to both sides.


-2y=-8 Combine like terms on the right side.


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


y=4 Reduce.


So the solutions are x=-1 and y=4.


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 -3x%2By=7 (red) and 5x%2B2y=3 (green)
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