Linear equations

A linear equation is an algebraic equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. When this equation is graphed, it always results in a straight line. Hence it is named as a 'linear' equation.

The standard form of a linear equation in one variable is of the form $ax+b=0$. Here, $x$ is a variable, $a$ is a coefficient and $b$ is constant. The standard form of a linear equation in two variables is of the form $ax+by=c$ . Here, $x$ and $y$ are variables, $a$ and $b$ are coefficients and $c$ is a constant.

Example for linear equation in one variable $5x+6=0$

Example for linear equation in two variables $5x+6y+7=0$

Problem 1:

Write each of the following equation in the form ax + by + c = 0 and indicate the values of a, b and c in each case:

$4=5x-3y$

Solution:

$5x-3y-4=0$ , Here $a=5,b=-3,c=-4$

Problem 2:

Write each of the following as an equation in two variables.

(i) $x=-5$ ----- $1.x+0.y+5=0$

(i) $5y=2$ ----- $0.x+5.y-2=0$