1. Chapter 6 Conic Sections
Nonlinear Systems of Equations

2. Nonlinear Systems of Equations
The graphs of the equations in a nonlinear system of equations can have no point of intersection or one or more points of intersection.
The coordinates of each point of intersection represent a solution of the system of equations.
When no point of intersection exists, the system of equations has no real-number solution.
We can solve nonlinear systems of equations by using the substitution or elimination method.

3. Example
Solve the following system of equations:

4. Example continued
We use the substitution method.
First, we solve equation (2) for y.

5. Example continued
Next, we substitute y = 2x  3 in equation (1) and solve for x:

6. Example continued
Now, we substitute these numbers for x in equation (2) and solve for y.
x = x = 12 / 5

7. Example continued
Check: (0, 3)
Check:
Visualizing the Solution

8. Example
Solve the following system of equations:
xy = 4
3x + 2y = 10

9. Example continued
Solve xy = 4 for y.
Substitute into 3x + 2y = 10.

10. Use the quadratic formula to solve:
Example continued
Use the quadratic formula to solve:

11. Visualizing the Solution
Example continued
Substitute values of x to find y.
3x + 2y = 10
x = 4/ x = 2
The solutions are
Visualizing the Solution

12. Example
Solve the system of equations:

13. Example continued
Solve by elimination.

14. Example continued
Substituting x = 1 in equation (2) gives us:
x = x = -1
The possible solutions are

15. Example continued All four pairs check, so they are the solutions.
Visualizing the Solution