1. Topic: U4L2 Solving Nonlinear Systems of Equations EQ: How can I solve a system of equations if one or more of the equations does not represent a line?

2.  System – 2 or more equations together  Solution of system – any ordered pair that makes all equations true  Possible solutions: 1. One point 2. More than one point 3. No solution 4. Infinite solutions Review – What?

3. Review - How?  What methods have we used to solve linear systems of equations? 1. Graphing 2. Substitution

4. Review Steps for using SUBSTITUTION 1. Solve one equation for one variable. (Hint: Look for an equation already solved for a variable or for a variable with a coefficient of 1 or -1.) 2. Substitute into the other equation. 3. Solve this equation to find a value for the variable. 4. Substitute again to find the value of the other variable. 5. Check.

5. Review Solve using Substitution. 2x – y = 6 y = 5x

6. What’s New?  A non-linear system is one in which one or more of the equations has a graph that is not a line.  With non-linear systems, the solution could be one or more points of intersection or no point of intersection.  We’ll solve non-linear systems using substitution.  A graph of the system will show the points of intersection.

7.  Solve the following system of equations : An Example…

8.  We use the substitution method. First, we solve equation (2) for y.

9. An Example…  Next, we substitute y = 2x  3 in equation (1) and solve for x:

10. An Example… …  Now, we substitute these numbers for x in equation (2) and solve for y.  x = 0x = 12 / 5 y = 2x  3 y = 2(0)  3 y = 3 SOLUTIONS (0, 3) and

11. An Example… Check: (0, 3) Check:  Visualizing the Solution

12. Example 1 Solve by substitution.  x 2 = y – 1  4x – y = -1

13. Example 2  Solve by substitution. x + 2y = 0 (x – 1) 2 + (y – 1) 2 = 5

14. Another example to watch…  Solve the following system of equations: xy = 4 3x + 2y = 10