SOLUTION: Solve the system by addition: 5x+y= -2 3x-2y= 4

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Question 376340: Solve the system by addition:
5x+y= -2
3x-2y= 4
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%285x%2By=-2%2C3x-2y=4%29


2%285x%2By%29=2%28-2%29 Multiply the both sides of the first equation by 2.


10x%2B2y=-4 Distribute and multiply.


So we have the new system of equations:
system%2810x%2B2y=-4%2C3x-2y=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:


%2810x%2B2y%29%2B%283x-2y%29=%28-4%29%2B%284%29


%2810x%2B3x%29%2B%282y%2B-2y%29=-4%2B4 Group like terms.


13x%2B0y=0 Combine like terms.


13x=0 Simplify.


x=%280%29%2F%2813%29 Divide both sides by 13 to isolate x.


x=0 Reduce.


------------------------------------------------------------------


10x%2B2y=-4 Now go back to the first equation.


10%280%29%2B2y=-4 Plug in x=0.


0%2B2y=-4 Multiply.


2y=-4-0 Subtract 0 from both sides.


2y=-4 Combine like terms on the right side.


y=%28-4%29%2F%282%29 Divide both sides by 2 to isolate y.


y=-2 Reduce.


So the solutions are x=0 and y=-2.


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 5x%2By=-2 (red) and 3x-2y=4 (green)


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

Also, feel free to check out my tutoring website

Jim