SOLUTION: 3x-2y=4 2x-5y=21

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Question 153100: 3x-2y=4
2x-5y=21
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=4%2C2x-5y=21%29


-2%283x-2y%29=-2%284%29 Multiply the both sides of the first equation by -2.


-6x%2B4y=-8 Distribute and multiply.


3%282x-5y%29=3%2821%29 Multiply the both sides of the second equation by 3.


6x-15y=63 Distribute and multiply.


So we have the new system of equations:
system%28-6x%2B4y=-8%2C6x-15y=63%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:


%28-6x%2B4y%29%2B%286x-15y%29=%28-8%29%2B%2863%29


%28-6x%2B6x%29%2B%284y%2B-15y%29=-8%2B63 Group like terms.


0x%2B-11y=55 Combine like terms. Notice how the x terms cancel out.


-11y=55 Simplify.


y=%2855%29%2F%28-11%29 Divide both sides by -11 to isolate y.


y=-5 Reduce.


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-6x%2B4y=-8 Now go back to the first equation.


-6x%2B4%28-5%29=-8 Plug in y=-5.


-6x-20=-8 Multiply.


-6x=-8%2B20 Add 20 to both sides.


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


x=%2812%29%2F%28-6%29 Divide both sides by -6 to isolate x.


x=-2 Reduce.


So our answer is x=-2 and y=-5.


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-2y=4 (red) and 2x-5y=21 (green)