SOLUTION: i need step by step solution using elimination x+y=-12 x-y=-4

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Question 148094This question is from textbook
: i need step by step solution using elimination
x+y=-12
x-y=-4 This question is from textbook

Found 2 solutions by jim_thompson5910, mangopeeler07:
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%28x%2By=-12%2Cx-y=-4%29


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


%28x%2By%29%2B%28x-y%29=%28-12%29%2B%28-4%29


%28x%2Bx%29%2B%28y-y%29=-12%2B-4 Group like terms.


2x%2B0y=-16 Combine like terms. Notice how the y terms cancel out.


2x=-16 Simplify.


x=%28-16%29%2F%282%29 Divide both sides by 2 to isolate x.


x=-8 Reduce.


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


x%2By=-12 Now go back to the first equation.


-8%2By=-12 Plug in x=-8.


-8%2By=-12 Multiply.


y=-12%2B8 Add 8 to both sides.


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


So our answer is x=-8 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 x%2By=-12 (red) and x-y=-4 (green)

Answer by mangopeeler07(462) About Me  (Show Source):
You can put this solution on YOUR website!
x%2By=-12
x-y=-4
Since the y's in the expressions are opposites, then just add the expressions to each other to eliminate the y variable from the jump.

x%2By=-12
+x-y=-4
----------------
2x+=-16

Then divide both sides by 2
x=-8

Then to get y, plug x back into one of the original equations x%2By=-12 or
x-y=-4. Doesn't matter which one. How about x%2By=-12.

Plug in -8 for x
-8%2By=-12.

Then add 8 to each side
y=-4.

Plug both values into the other original equation x-y=-4.
-8--4=-4 or -8%2B4=-4. It's true.

Therefore,
x=-8
y=-4