# Difference Between Linear and Non-linear Equations

An equation is nothing but a statement that defines the equality between two or more expressions. The equation is denoted by the ‘equal to’ sign. The part of the equation towards the left side is known as the left-hand side (LHS), and the part inclined towards the right is (RHS) right-hand side. An equation contains both variables as well as constant. Both need not be present, but one of these mathematical terms is vital for forming an equation.

For example, 20a + 3c = 12, this is an ideal example of an equation. Here ‘a’ and ‘c’ are known as the variable, and ‘12’ is known as the constant of this equation. 20a + 3c is the LHS of the equation, while 12 is the RHS. It must be noted that the same mathematical operations are carried out on both sides of the equation. This is one of the most important rules for solving an equation. If, for instance, you want to multiply the LHS by two, then the RHS shall also be multiplied by 2. This ensures that the equation always remains the same.

Now that we have a basic understanding of an equation let us look into different types of equations in mathematics. The equations are categorized as linear or non-linear equations based on the degree and variable in the equations.

Degree of an equation: The maximum power of the variable in the algebraic statement is the degree of polynomials in one variable. For instance, consider the following equation: x3 + 11x + 21. The equation's degree is three, which is the largest power of the variable in the equation.

The difference between the two types of equations is tabulated below:

 Linear Equation Non-Linear Equation A linear equation is one in which the greatest degree of a term is one. An equation with only one variable is sometimes known as a linear equation in one variable. A non-linear equation is one in which the greatest degree of a term is 2 or more than 2. When the results of a linear equation are displayed on a graph, they create a straight line. When the results of a non-linear equation are displayed on a graph, they create curves like parabola, hyperbola, or ellipse. A linear equation has the generic form kx + l = m, where k, l, and m are constants, and x is the only variable. A linear equation has the generic form mx2 + ny2 = d, where d, m, and n are constants, and x and y are variables. For example:  x + 13 = 1, x/2 – 3 = 5 are equation in one variable x and here the highest degree of each equation is one.  a + 7b = 21, 7a - b/2 = 5 are linear equations in two variables a and b. For example:   12x2 + 44x + 1 = 23, this are the example of non-linear equations, because this equation has highest degree of 2.   2x + y = 15, is nonlinear because it has variable x and y.

NCERT Class 9 Maths Chapter 4 Linear Equations in Two Variables is one of the most important chapters in Class 9, it extensively talks about linear equations, non-linear equations, the difference between them, and other important theorems.

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