Non-linear systems are just systems of equations where one or more of the equations is not linear.

Some common non-linear systems as pictures:

And as equations:

$$x^2+3x+y^2+2y=25$$

$$x^3+x-7$$

$$x^2+x-4$$

Example problem:

$${y=x}^2+4x+3$$

$$y=-x-3$$

If ((x,;y)) is a solution to the system above, and (xneq-2), what is the value of (3x)?

**Strategy****:**

**Enter the equations into Desmos****Identify all points of intersection. These are solutions common to the equations. There could be one, multiple, or no points of intersection. If there are no points of intersection we say there are “no solutions” to the system.**

Take the following example:

$$x^2+y^2=153$$

$$2y=-8x$$

If ((x,12)) is a solution to the systems of equations above, what is the value ofÂ (x^2)?

A) -51

B) 3

C) 9

D) 144

When we plug into Desmos, we can see the points of intersection.

The *x* value here is -3, but remember they asked us for: $$x^2$$ Always answer the question that is asked!

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