Introduction to linear equations — lesson. Mathematics CBSE, Class 8.

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The equation is a statement of equality that contains one or more unknown value or variables.

Example:

\begin{array}{l} The following are equations with 1 variable : \\ 9 x + 12 = 13, \\ y^{2} + 13 = 12, \\ \frac{13 x}{12} - \frac{9}{12} = 13 \end{array}

\begin{array}{l} The following are equations with 2 variable : \\ 9 x + 12 y = 13, \\ y^{2} + 13 x = 12, \\ \frac{13 x}{12} - \frac{9 y}{12} = 13 \end{array}

An equation is always equated to either a numerical value or another algebraic expression.

Now we understood what an equation is. Then we will see about linear equation.

An equation involving only linear polynomial is called a simple equation or a simple linear equation.

The highest power of the variable in the linear equation should be one. If the power of the variable is more than one that is not considered as a linear equation.

In linear equation the highest power of the variable = 1

Example:

\begin{array}{l} The following are linear equations : \\ 9 x + 12 = 13, \\ 13 x = 12, \\ \frac{13 x}{12} - \frac{9}{12} = 13 \end{array}

\begin{array}{l} The following are not linear equations : \\ 9 x^{2} + 12 y = 13, \\ y^{2} + 13 x = 12, \\ \frac{13 y^{2}}{12} + \frac{12}{9} y = 9 . \end{array}

In upcoming exercises, we will deal with equations with linear expressions in one variable only. Such equations are known as linear equations in one variable.

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1. Introduction to linear equations

Theory: