NON LINEAR EQUATIONS
Definition Of Nonlinear Equations
Equation whose graph does not form a straight line (linear) is called a Nonlinear Equation
More About Nonlinear Equations
In a nonlinear equation, the variables are either of degree greater than 1 or less than 1, but never 1.
Example of Nonlinear Equations
4x2 + 2y - 1 = 0 and x3 + 2x2 - 4xy - 1 = 0 are the examples of nonlinear equations.
is a nonlinear equation.
Video Examples: Linear and NonLinear Equations
Solved Example on Nonlinear Equations
Ques: Which of the following equations is not a linear equation?
Choices:
A. 3x - 5 = 8x
B. 2 + 3x = 4
C. (x + 2)2 = 6
D. x = 1
Correct Answer: C
Solution:
Step 1: An algebraic equation is said to be linear if the variable or variables in the equation are of first degree.
Step 2: In the equation (x + 2)2 = 6, x is raised to the power 2.
Step 3: So, (x + 2)2 = 6 is not a linear equation.
Quick Summary
- Nonlinear equations involve variables with degrees other than 1.
- Examples include equations with exponents or variables multiplied together.
🍎 Teacher Insights
Emphasize the graphical representation of nonlinear equations to illustrate their deviation from straight lines. Use examples to show the effect of different exponents on the shape of the graph.🎓 Prerequisites
- Linear Equations
- Exponents
- Algebraic Expressions
Check Your Knowledge
Q1: Which of the following is a nonlinear equation?
Frequently Asked Questions
Q: What is the difference between a linear and nonlinear equation?
A: A linear equation forms a straight line when graphed, while a nonlinear equation does not. Nonlinear equations often contain variables raised to powers other than 1.