Systems of Nonlinear Equations

Hey everyone! It's Shelly and I'm scribing for friday December 16. First off before I start, I hope everyone had an amazing weekend! (: Last class we learned how to solve systems of nonlinear equations graphically and algebraically.

Solving Systems of Equations Graphically

There are 4 different types of conics: circle, eclipse, parabolas, and hyperboblas

circle

eclipse

parabola

hyperbola

In a linear-quadratic system of equation, it includes one of the conics and a linear equation.The solution of the two equations in two variables would still correspond to a point of intersection of their graphs.There are three possible outcomes for these types of systems.

 1. there could be no solutions which means they dont intersect

example:

 2. there could be 1 solution which means they intersect in only 1 spot

example:

3. there could be 2 solutions which means they could intersect in 2 spots

example:

Example:

Take the first equation and solve for y using the table of values.

The graph will look like this:

Now take the second equation and solve by using the formula:

which would equal:

Now that we know what x is, fill in the second equation and solve for y

Since we know the vertex is (2,2) we can graph it.

There are 2 solutions (1,4) and (5,8)

Here's a video to help you guys to understand better (:

 

Solving Systems of Equations Algebraically

Solve by using substitution and elimination.

Example:

Take the first equation and isolate y

Take the second equation and plug in for y

which will be:

Now factor

Move the numbers to the other side

Take the first equation and fill in for x

Your final answers are:

I hope this helped you guys! (: