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

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Presentation transcript:

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

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

Solving Systems of non linear Equations

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.

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

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

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

Solving Systems by Graphing Solve: y = x2 + 3 2. 4x3 - 4y = 12 y - 3x = -2 x – y = 3 1. X = 1, y = 1; 2. x=1, y=-2