SOLUTION: 6x -y =-8 2x + y =-16 im getting stuck the first step! try to solve by elimination method

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Question 585447: 6x -y =-8
2x + y =-16
im getting stuck the first step!
try to solve by elimination method
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%286x-y=-8%2C2x%2By=-16%29


Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%286x-y%29%2B%282x%2By%29=%28-8%29%2B%28-16%29


%286x%2B2x%29%2B%28-y%2By%29=-8%2B-16 Group like terms.


8x%2B0y=-24 Combine like terms.


8x=-24 Simplify.


x=%28-24%29%2F%288%29 Divide both sides by 8 to isolate x.


x=-3 Reduce.


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6x-1y=-8 Now go back to the first equation.


6%28-3%29-1y=-8 Plug in x=-3.


-18-y=-8 Multiply.


-y=-8%2B18 Add 18 to both sides.


-y=10 Combine like terms on the right side.


y=%2810%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=-10 Reduce.


So the solutions are x=-3 and y=-10.


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 6x-y=-8 (red) and 2x%2By=-16 (green)


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