I'm going to chose to use the substitution method.

Not that because of the terms involved, it would not be possible to
work this problem using the process of elimination.

Both of these equations are already simplified. No work needs
to be done here.

It does not matter which equation or which variable you choose to solve
for. Just keep it simple.

I'm going to chose to use the first equation to solve for *y*.

**Solving the first equation for y we get:**

***1st equation solved for y**

(when you plug in an expression like this, it is just like you plug in a number for your variable)

***Factor
the difference of squares**

***Set 1st factor = 0**

***Set 2nd factor = 0**

Plug in both values found for *x* in step
4.

**Plug in 2 for x into the equation in
step 2 to find y's value.**

You will find that if you plug either the ordered pair (-2, -2) OR
(2, 2) into BOTH equations of the original system, that they are both a
solution to BOTH of them.

**(-2, -2) and (2, 2) are both a solution to our system.**

I'm going to chose to use the elimination by addition method, however
it would be perfectly find for you to use the substitution method.
Either way the answer will be the same.

Both of these equations are already simplified. No work needs
to be done here.

Again, you want to make this as simple as possible.

**The variable that you want to eliminate must be a like variable. **Note that *x* squareds' coefficients are
already opposites. So we do not have to multiply either equation
by a number.

Also note that the *y* terms are not like
terms so we would not be able to eliminate *y* in this problem.

**Here is the original problem complete with opposite coefficients
for the x squared terms:**

Note that this does not factor, so I'm going to have to use drastic
majors - yes the Quadratic Formula.

If you need a review on the quadratic formula feel free to go to **Tutorial
17: Quadratic Equations.**

***Identifying a, b, and c**

***Plugging a, b,
and c into the quad form.**

***Simplifying radicand, which is a negative
number**

Note how we came up with a negative underneath the square root.

**That means there is NOT a real number solution for this.**

There is no value to plug in here.

There are no ordered pairs to check.

**The answer is no solution.**

I'm going to chose to use the substitution method, however it would
be perfectly find for you to use the elimination by addition method.
Either way the answer will be the same.

Both of these equations are already simplified. No work needs
to be done here.

Note how the first equation is already solved for *y*.
We can use that one for this step.

It does not matter which equation or which variable you choose to solve for. But it is to your advantage to keep it as simple as possible.

**First equation solved for y:**

(when you plug in an expression like this, it is just like you plug in a number for your variable)

***Variable dropped out AND true**

As mentioned before, if the variable drops out AND we have a TRUE statement,
then when have an infinite number of solutions. They end up being
the same line.

Since we did not get a value for *x*, there
is nothing to plug in here.

There is no value to plug in here.

When they end up being the same equation, you have an infinite number of solutions. You can write up your answer by writing out either equation to indicate that they are the same equation.

**Two ways to write the answer are OR .**

Last revised on April 25, 2011 by Kim Seward.

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