1. 3.5 Solving Nonlinear Systems

2. System of Nonlinear Equations
At least one equation is non-linear.
1 quadratic & 1 linear
ex.
both quadratic
Graph of equations can intersect at zero, one, or two points.
zero points
one point
two points

3. Solving by Graphing Example 1
1) Graph both equations on the same graph.
2) Estimate the point of intersection.
3) Check the point by substituting the coordinates back into the original equations.
The solution is

4. Solve by Elimination Example 2
Add the equations to eliminate the -term.
Obtain a quadratic equation for .
Solve for with the quadratic formula.
No negative numbers inside
No real solution.

5. Solve By Substitution Example 3
1) Substitute for in the first equation and solve for .
2) Substitute the solutions in
to solve for .

6. Solve By Substitution Example 4
Substitute for in the first equation and solve for .
Substitute the solutions in
to solve for .
Solution:

7. Solving Quadratic Equations by Graphing Example 5

8. Solving Quadratic Equations by Graphing Example 5 Second Method