UPSKILL MATH PLUS

Learn Mathematics through our AI based learning portal with the support of our Academic Experts!

Learn moreEquation:

Before we study about the linear equations, first do you have any idea about what is an equation?

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

Example:

$\begin{array}{l}\mathit{Equations}\phantom{\rule{0.147em}{0ex}}\mathit{with}\phantom{\rule{0.147em}{0ex}}1\phantom{\rule{0.147em}{0ex}}\mathit{variable}:\\ \\ i)\phantom{\rule{0.147em}{0ex}}10x+9=6,\\ \\ \mathit{ii})\phantom{\rule{0.147em}{0ex}}{y}^{2}+6=9,\\ \\ \mathit{iii})\phantom{\rule{0.147em}{0ex}}\frac{6x}{9}-\frac{10}{9}=6.\end{array}$

$\begin{array}{l}\mathit{Equations}\phantom{\rule{0.147em}{0ex}}\mathit{with}\phantom{\rule{0.147em}{0ex}}2\phantom{\rule{0.147em}{0ex}}\mathit{variable}:\\ \\ i)\phantom{\rule{0.147em}{0ex}}10x+9y=6,\\ \\ \mathit{ii}){y}^{2}+6x=9,\\ \\ \mathit{iii})\phantom{\rule{0.147em}{0ex}}\frac{6x}{9}-\frac{10y}{9}=6.\end{array}$

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

**Equal sign**\((=)\):

The equality sign shows that the value of the expression to the left of the \((=)\) sign is equal to the value of the expression to the right of the \((=)\) sign.

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

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

Simple equation:

If the linear equation contains one as the highest power of the variable, then that linear equation is called the simple equation or simple linear equation.

If the power of the variable is more than one that is not considered as a simple equation.

$\mathit{In}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{simple}\phantom{\rule{0.147em}{0ex}}\mathit{equation}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{highest}\phantom{\rule{0.147em}{0ex}}\mathit{power}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{variable}\phantom{\rule{0.147em}{0ex}}=1$

$\begin{array}{l}\mathit{These}\phantom{\rule{0.147em}{0ex}}\mathit{are}\phantom{\rule{0.147em}{0ex}}\mathit{simple}\phantom{\rule{0.147em}{0ex}}\mathit{equations}:\\ \\ i)\phantom{\rule{0.147em}{0ex}}10x+9=6,\\ \\ \mathit{ii})\phantom{\rule{0.147em}{0ex}}6x=9,\\ \\ \mathit{iii})\phantom{\rule{0.147em}{0ex}}\frac{6x}{9}-\frac{10}{9}=6\end{array}$

$\begin{array}{l}\mathit{These}\phantom{\rule{0.147em}{0ex}}\mathit{are}\phantom{\rule{0.147em}{0ex}}\mathit{not}\phantom{\rule{0.147em}{0ex}}\mathit{simple}\phantom{\rule{0.147em}{0ex}}\mathit{equations}:\\ \\ I)\phantom{\rule{0.147em}{0ex}}10{x}^{2}+9y=6,\\ \\ {\mathit{II})\phantom{\rule{0.147em}{0ex}}y}^{2}+6x=9,\\ \\ \mathit{III})\phantom{\rule{0.147em}{0ex}}\frac{6{y}^{2}}{9}+\frac{9}{10}y=10,\end{array}$

Here we will deal with equations with simple linear expressions in one variable only.

**Such equations are known as simple equations in one variable.**