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# Linear Equation Formula

Linear equation are important topic in maths. Lets check out Linear Equation Formula which consist for formula for one variable linear equation, two variable linear equation and three variable linear equation

## Algebraic Equation

An algebraic equation is an equality involving variables. It says that the value of the expression on one side of the equality sign is equal to the value of the expression on the other side

## What is Linear equation in one Variable

We will restrict the above equation with two conditions

(a) algebraic equation in one variable
(b) variable will have power 1 only

or

An equation of the form ax + b = 0, where a and b are real numbers, such that a is not equal to zero, is called a linear equation in one variables

Linear equation in One variable has only one Solution. It can be solved as given below

## What is Linear equation in two Variable

$ax+by+c=0$, $a \neq 0$ and $b \neq 0$

• a, b and c are real number
• Infinite solution possible
• Linear equation in two variables is represented by straight line the Cartesian plane.
• Every point on the line is the solution of the equation.
• For $ax+by+c=0 \; , \; a \neq 0 \; and \; b \neq 0$. The point on Y-axis is given $(0,\frac{-c}{b})$ . The point on X-axis is given by $(\frac {-c}{a}, 0)$

## Simultaneous pair of Linear equation

A pair of Linear equation in two variables
$a_1 x + b_1 y + c_1=0$
$a_2 x + b_2 y + c_2=0$
Graphically it is represented by two straight lines on Cartesian plane

Here is the Graphical Representation

Algebraic Solution of system of Linear equation

## What is Linear equation in three Variable

$ax+by+cz +d=0$, $a \neq 0$ , $b \neq 0$ and $c \neq 0$

• a, b and c are real number
• Infinite solution possible
• Linear equation in three variables is represented by straight line the three-dimensional Cartesian plane.
• Every point on the line is the solution of the equation.

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