Nonlinear Systems Warm Up Solve each quadratic equation
![Nonlinear Systems Warm Up Solve each quadratic equation by factoring. Check your answer. 5, Nonlinear Systems Warm Up Solve each quadratic equation by factoring. Check your answer. 5,](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-1.jpg)
![Nonlinear Systems Recall that a system of linear equations is a set of two Nonlinear Systems Recall that a system of linear equations is a set of two](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-2.jpg)
![Nonlinear Systems A system made up of a linear equation and a quadratic equation Nonlinear Systems A system made up of a linear equation and a quadratic equation](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-3.jpg)
![Nonlinear Systems Example 1: Solving a Nonlinear System by Graphing Solve the system by Nonlinear Systems Example 1: Solving a Nonlinear System by Graphing Solve the system by](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-4.jpg)
![Nonlinear Systems Check It Out! Example 1 1. Solve the system by graphing. Check Nonlinear Systems Check It Out! Example 1 1. Solve the system by graphing. Check](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-5.jpg)
![Nonlinear Systems Remember! The substitution method is a good choice when either equation is Nonlinear Systems Remember! The substitution method is a good choice when either equation is](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-6.jpg)
![Nonlinear Systems Example 2: Solving a Nonlinear system by substitution. Solve the system by Nonlinear Systems Example 2: Solving a Nonlinear system by substitution. Solve the system by](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-7.jpg)
![Nonlinear Systems Example 2: Continued The solutions are (4, 15) and (2, – 3). Nonlinear Systems Example 2: Continued The solutions are (4, 15) and (2, – 3).](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-8.jpg)
![Nonlinear Systems Check It Out! Example 2 1. Solve the system by substitution. Check Nonlinear Systems Check It Out! Example 2 1. Solve the system by substitution. Check](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-9.jpg)
![Nonlinear Systems Check It Out! Example 2 Continued The solutions are ( – 1, Nonlinear Systems Check It Out! Example 2 Continued The solutions are ( – 1,](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-10.jpg)
![Nonlinear Systems Remember! The elimination method is a good choice when both equations have Nonlinear Systems Remember! The elimination method is a good choice when both equations have](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-11.jpg)
![Nonlinear Systems Example 3 : Solving a Nonlinear System by Elimination. Solve each system Nonlinear Systems Example 3 : Solving a Nonlinear System by Elimination. Solve each system](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-12.jpg)
![Nonlinear Systems Example 3 : Continued The solution is (– 3, – 10 ) Nonlinear Systems Example 3 : Continued The solution is (– 3, – 10 )](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-13.jpg)
![Nonlinear Systems Example 3 : Continued B y = 2 x 2 + x Nonlinear Systems Example 3 : Continued B y = 2 x 2 + x](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-14.jpg)
![Nonlinear Systems Example 3 : Continued - 1 ± √– 63 x= 8 Holt Nonlinear Systems Example 3 : Continued - 1 ± √– 63 x= 8 Holt](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-15.jpg)
![Nonlinear Systems Check It Out! Example 3 1. Solve each system by elimination. Check Nonlinear Systems Check It Out! Example 3 1. Solve each system by elimination. Check](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-16.jpg)
![Nonlinear Systems Check It Out! Example 3 Continued The solution is (3, 4) and Nonlinear Systems Check It Out! Example 3 Continued The solution is (3, 4) and](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-17.jpg)
![Nonlinear Systems Remember! The elimination method is a good choice when both equations have Nonlinear Systems Remember! The elimination method is a good choice when both equations have](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-18.jpg)
![Nonlinear Systems Lesson Quiz: Part-1 Solve each system by the indicated method. 1. Graphing: Nonlinear Systems Lesson Quiz: Part-1 Solve each system by the indicated method. 1. Graphing:](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-19.jpg)
![Nonlinear Systems Lesson Quiz: Part-2 3. Elimination: y = x 2 + 2 x Nonlinear Systems Lesson Quiz: Part-2 3. Elimination: y = x 2 + 2 x](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-20.jpg)
- Slides: 20
![Nonlinear Systems Warm Up Solve each quadratic equation by factoring Check your answer 5 Nonlinear Systems Warm Up Solve each quadratic equation by factoring. Check your answer. 5,](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-1.jpg)
Nonlinear Systems Warm Up Solve each quadratic equation by factoring. Check your answer. 5, -2 -2 Find the number of real solutions of each equation using the discriminant. 3. 25 x 2 - 10 x + 1 = 0 one 1. x 2 - 3 x - 10 = 0 2. -3 x 2 - 12 x = 12 4. 2 x 2 + 7 x + 2 = 0 two 5. 3 x 2 + x + 2 = 0 none Holt Mc. Dougal Algebra 1
![Nonlinear Systems Recall that a system of linear equations is a set of two Nonlinear Systems Recall that a system of linear equations is a set of two](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-2.jpg)
Nonlinear Systems Recall that a system of linear equations is a set of two or more linear equations. A solution of a system is an ordered pair that satisfies each equation in the system. Points where the graphs of the equations intersect represent solutions of the system. A nonlinear system of equations is a system in which at least one of the equations is nonlinear. For example, a system that contains one quadratic equation and one linear equation is a nonlinear system. Holt Mc. Dougal Algebra 1
![Nonlinear Systems A system made up of a linear equation and a quadratic equation Nonlinear Systems A system made up of a linear equation and a quadratic equation](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-3.jpg)
Nonlinear Systems A system made up of a linear equation and a quadratic equation can have no solution, one solution, or two solutions, as shown below. Holt Mc. Dougal Algebra 1
![Nonlinear Systems Example 1 Solving a Nonlinear System by Graphing Solve the system by Nonlinear Systems Example 1: Solving a Nonlinear System by Graphing Solve the system by](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-4.jpg)
Nonlinear Systems Example 1: Solving a Nonlinear System by Graphing Solve the system by graphing. Check your answer. y = x 2 + 4 x + 3 y=x+3 Holt Mc. Dougal Algebra 1
![Nonlinear Systems Check It Out Example 1 1 Solve the system by graphing Check Nonlinear Systems Check It Out! Example 1 1. Solve the system by graphing. Check](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-5.jpg)
Nonlinear Systems Check It Out! Example 1 1. Solve the system by graphing. Check your answer. y = x 2 - 4 x + 5 y=x+1 Holt Mc. Dougal Algebra 1
![Nonlinear Systems Remember The substitution method is a good choice when either equation is Nonlinear Systems Remember! The substitution method is a good choice when either equation is](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-6.jpg)
Nonlinear Systems Remember! The substitution method is a good choice when either equation is solved for a variable, both equations are solved for the same variable, or a variable in either equation has a coefficient of 1 or -1. Holt Mc. Dougal Algebra 1
![Nonlinear Systems Example 2 Solving a Nonlinear system by substitution Solve the system by Nonlinear Systems Example 2: Solving a Nonlinear system by substitution. Solve the system by](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-7.jpg)
Nonlinear Systems Example 2: Solving a Nonlinear system by substitution. Solve the system by substitution. y = x 2 - x - 5 y = -3 x + 3 Holt Mc. Dougal Algebra 1
![Nonlinear Systems Example 2 Continued The solutions are 4 15 and 2 3 Nonlinear Systems Example 2: Continued The solutions are (4, 15) and (2, – 3).](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-8.jpg)
Nonlinear Systems Example 2: Continued The solutions are (4, 15) and (2, – 3). Holt Mc. Dougal Algebra 1
![Nonlinear Systems Check It Out Example 2 1 Solve the system by substitution Check Nonlinear Systems Check It Out! Example 2 1. Solve the system by substitution. Check](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-9.jpg)
Nonlinear Systems Check It Out! Example 2 1. Solve the system by substitution. Check your answer. y = 3 x 2 - 3 x + 1 y = -3 x + 4 Holt Mc. Dougal Algebra 1
![Nonlinear Systems Check It Out Example 2 Continued The solutions are 1 Nonlinear Systems Check It Out! Example 2 Continued The solutions are ( – 1,](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-10.jpg)
Nonlinear Systems Check It Out! Example 2 Continued The solutions are ( – 1, 7) and (1, 1). Holt Mc. Dougal Algebra 1
![Nonlinear Systems Remember The elimination method is a good choice when both equations have Nonlinear Systems Remember! The elimination method is a good choice when both equations have](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-11.jpg)
Nonlinear Systems Remember! The elimination method is a good choice when both equations have the same variable term with the same or opposite coefficients or when a variable term in one equation is a multiple of the corresponding variable term in the other equation. Holt Mc. Dougal Algebra 1
![Nonlinear Systems Example 3 Solving a Nonlinear System by Elimination Solve each system Nonlinear Systems Example 3 : Solving a Nonlinear System by Elimination. Solve each system](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-12.jpg)
Nonlinear Systems Example 3 : Solving a Nonlinear System by Elimination. Solve each system by elimination. A 3 x - y = 1 y = x 2 + 4 x - 7 Holt Mc. Dougal Algebra 1
![Nonlinear Systems Example 3 Continued The solution is 3 10 Nonlinear Systems Example 3 : Continued The solution is (– 3, – 10 )](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-13.jpg)
Nonlinear Systems Example 3 : Continued The solution is (– 3, – 10 ) and (2, 5). Holt Mc. Dougal Algebra 1
![Nonlinear Systems Example 3 Continued B y 2 x 2 x Nonlinear Systems Example 3 : Continued B y = 2 x 2 + x](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-14.jpg)
Nonlinear Systems Example 3 : Continued B y = 2 x 2 + x - 1 x - 2 y = 6 Holt Mc. Dougal Algebra 1
![Nonlinear Systems Example 3 Continued 1 63 x 8 Holt Nonlinear Systems Example 3 : Continued - 1 ± √– 63 x= 8 Holt](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-15.jpg)
Nonlinear Systems Example 3 : Continued - 1 ± √– 63 x= 8 Holt Mc. Dougal Algebra 1 Since the discriminant is negative, there are no real solutions
![Nonlinear Systems Check It Out Example 3 1 Solve each system by elimination Check Nonlinear Systems Check It Out! Example 3 1. Solve each system by elimination. Check](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-16.jpg)
Nonlinear Systems Check It Out! Example 3 1. Solve each system by elimination. Check your answers. . a 2 x - y = 2 y = x 2 - 5 Holt Mc. Dougal Algebra 1
![Nonlinear Systems Check It Out Example 3 Continued The solution is 3 4 and Nonlinear Systems Check It Out! Example 3 Continued The solution is (3, 4) and](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-17.jpg)
Nonlinear Systems Check It Out! Example 3 Continued The solution is (3, 4) and (– 1, – 4). Holt Mc. Dougal Algebra 1
![Nonlinear Systems Remember The elimination method is a good choice when both equations have Nonlinear Systems Remember! The elimination method is a good choice when both equations have](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-18.jpg)
Nonlinear Systems Remember! The elimination method is a good choice when both equations have the same variable term with the same or opposite coefficients or when a variable term in one equation is a multiple of the corresponding variable term in the other equation. Holt Mc. Dougal Algebra 1
![Nonlinear Systems Lesson Quiz Part1 Solve each system by the indicated method 1 Graphing Nonlinear Systems Lesson Quiz: Part-1 Solve each system by the indicated method. 1. Graphing:](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-19.jpg)
Nonlinear Systems Lesson Quiz: Part-1 Solve each system by the indicated method. 1. Graphing: 2. Substitution: Holt Mc. Dougal Algebra 1 y = x 2 - 4 x + 3 y=x-1 y = 2 x 2 - 9 x - 5 y = -3 x + 3 (1, 0), (4, 3) (-1, 6), (4, -9)
![Nonlinear Systems Lesson Quiz Part2 3 Elimination y x 2 2 x Nonlinear Systems Lesson Quiz: Part-2 3. Elimination: y = x 2 + 2 x](https://slidetodoc.com/presentation_image_h/150fae6691f28cb64b3a919cd02e06ee/image-20.jpg)
Nonlinear Systems Lesson Quiz: Part-2 3. Elimination: y = x 2 + 2 x - 3 x-y=5 no solution 4. Elimination: y = x 2 - 7 x + 10 2 x - y = 8 (3, -2), (6, 4) Holt Mc. Dougal Algebra 1
Is quadratic equation nonlinear
Solving linear quadratic systems
The quadratic formula
How to solve a quadratic equation
What formula can be used to solve any quadratic equation
Fibo series
How to find the discriminant
Square root method
Quadratic equation examples
Solve each equation by substitution
Solving linear-quadratic systems by elimination
How to find discriminant
Solve the nonlinear inequality
Linear equation and quadratic equation
Solving systems of linear and quadratic equations
Graphing systems of nonlinear equations
Asymptotically stable
Nonlinear systems of equations worksheet
Solution of
Nonlinear ordinary differential equations
Difference between linear and nonlinear equations