3.5 Solving Nonlinear Systems

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Presentation transcript:

3.5 Solving Nonlinear Systems

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

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

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.

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

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

Solving Quadratic Equations by Graphing Example 5

Solving Quadratic Equations by Graphing Example 5 Second Method