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

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) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

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

Group like terms.

Combine like terms. Notice how the y terms cancel out.

Simplify.

Divide both sides by to isolate .

Reduce.

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

Now go back to the first equation.

Plug in .

Multiply.

Add to both sides.

Combine like terms on the right side.

So our answer is and .

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 (red) and (green)

Answer by mangopeeler07(462) (Show Source): You can put this solution on YOUR website!

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.

+
----------------

Then divide both sides by 2

Then to get y, plug x back into one of the original equations or
. Doesn't matter which one. How about .

Plug in -8 for x
.

Then add 8 to each side
.

Plug both values into the other original equation .
or . It's true.

Therefore,
x=-8
y=-4
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