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$$ax + b = 0$$ where

- • $x$ represents a variable or an unknown
- • a and b are constants
- • a ≠ 0

Note that the power (or exponent) of variable $x$ is 1. If the exponent of any variable is greater than 1, the equation is non-linear.

A linear equation in one variable can always be written as $$ax = b$$

If $a ≠ 0$, the above equation can be written as $$x = \frac{b}{a}$$

Here are some examples of linear equations

• $2x + 8 = 0$

• $\frac{m + 2}{4} + 5 = 9m$

Please note

• $9x^2 + 5 = 0$ is not a linear equation as $x^2$ term has a power greater than 1. It is a quadratic equation.

• $4y^{\frac{1}{3}} = 5$ is also not a linear equation as power of $y$ is not equal to 1

Consider the equation $ax + by + cz + d = 0$ where a, b, c and d are constants and a, b and c are ≠ 0.

This is also a linear equation but number of variables/unknowns are more than one.

A common form of linear equation in two variables $x$ and $y$ is written as $$y = mx + b$$ where $m$ and $b$ are constants.

The linear equation is called so as the solution of such equations form a

In the above equation $m$ represents

Here are some examples of linear equations with two variables:

• $2x - 5y = 0$

• $25c = 50d$

• $\frac{m + 2}{4 + n} + 5 = 9$

• First and the most important point to remember while solving an equation (linear or otherwise) is that whatever we do on one side of the $ “ = ” $ sign, the exact same things should be done on the other side of the sign.

While solving linear equations, we will make heavy use of this fact.

If a constant is added to Left Hand Side of the equation (

This is true for all operations - addition, subtraction, multiplication, division etc

• If there are fractions on one or both sides of the equation, use Least Common Denominator (LCD) to clear the fractions.

• Simplify both sides by solving brackets (parenthesis) and combining like terms.

• Try to isolate the variable.

Consider an equation

$4x - 8 = 0$

• Add 8 on each side

⇒ $4x - 8 + 8 = 8$ ⇒ $4x = 8$

• Divide both sides by 4

⇒ $\frac{4x}{4} = \frac{8}{4}$ ⇒ $x = 4$

We can check if our answer is right by placing this value of $x$ in the equation above.

$4x - 8 = 0$

$4 × 4 - 8 = 0$

$8 - 8 = 0$

$ 0 = 0 $

LHS and RHS tally. Hence our answer is right.

The values of m and b determine the slope and the y intercept of this line.

As we change the value of m and b, see how the slope and y intercept changes.

$y = x$ ⇒ For this line, slope is 1 (m = 1) and y intercept is 0 (b = 0). The line crosses y axis at (0,0).

$y = -x$ ⇒ For this line, slope is -1 (m = -1) and y intercept is 0 (b = 0). The line crosses y axis at (0,0).

$y = 2x + 2$ ⇒ For this line, slope is 2 (m = 2) and y intercept is 2 (b = 2). The line crosses y axis at (0,2).