1. Warm Up
3x + 5y = 25 4x + 7y = 34 Find the value of x and y so that both equations are true.

2. Answers
3x + 5y = 25 4x + 7y = 34 Find the value of x and y so that both equations are true. x = 5 y = 2

3. Solving Systems of non linear Equations

4. What is a system of equations?
A system of equations is two or more equations grouped together with the same set of unknowns. Ex. 6x + 5y = 3 2x + 9y = 2
Same set of unknowns, x and y.

5. What is the solution to a system of equations?
The solution of a system of equations is the set of variables that makes the system true.
Consider the previous example:
This is the solution to the system because these values make both equations true.
Ex. 6x + 5y = 3
2x + 9y = 2
x = 17/4
y = 3/22

6. There are multiple ways ways to solve systems of equations.
Today, we will just focus on graphing.
- graphing - substitution - elimination - matrices

7. Steps for Solving Systems by Graphing
Solve both equations for y.
Put the equations in your graphing calculator.
Use the INTERSECT tool to find where the equations share a point.
CAUTION: We will be looking at nonlinear systems (not just lines), so there may be more than one solution set.
1. X = 1, y = 1; 2. x=1, y=-2

8. Solving Systems by Graphing
Solve:
y = x x3 - 4y = 12
y - 3x = x – y = 3
1. X = 1, y = 1; 2. x=1, y=-2