SOLUTION: Solve by using elimination method. -4x-2y=3 2x+y=1 separate problem: 2x+y=1 -x-y=-3

Question 244763: Solve by using elimination method.
-4x-2y=3
2x+y=1

separate problem:
2x+y=1
-x-y=-3
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1

Start with the given system of equations:

Multiply the both sides of the second equation by 2.

Distribute and multiply.

So we have the new system of equations:

Now 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.

Simplify.

Since is NEVER true, this means that there are no solutions.

So the system is inconsistent.

# 2

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.

Simplify.

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

Now go back to the first equation.

Plug in .

Multiply.

Add to both sides.

Combine like terms on the right side.

So the solutions are 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)

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