Learn Online Linear

A statement in which two quantities are equal is called an equation.

Introduction to learn online linear:

An equation of the form `ax+b=0, a!=0` is called a linear equation in the variable x.When the degree of the variable on both sides equal to one, then it is a linear equation. It has more than one variable.

Linear equation is the equation of the form y = mx + b. The above equation involves two variables namely  x and  y. Linear equation is a type of algebraic equation, which consists of all variables of degree one and constants. Examples of linear equations are

`5x = 10`  Linear equation of one variable

`4x+7y = 10` Linear equation of two variables

`3x +7y+9z = 11` Linear equation of three variables

Solution of linear equation: Any value ( or values) of the variable (or variables) which when substitued in an equation makes its both sides equal is called a solution (or root ) of the equation.


Types of linear equation:


Conditional Equation:
If the linear equation has the real roots, it is called conditional.

Ex:

2x + 5 = 7

7x + 3 = 10

Unconditional Equation:
If the roots are not real, it is called unconditional.

Ex:

5x + 8 > 1

4x + 4 < 1

Quadratic Equation:
Quadratic is  the second degree of the polynomial equation

Ex:

4x2 + 2x + 4 = 9

Understanding Shapes with Obtuse Angles is always challenging for me but thanks to all math help websites to help me out.

Example problems on linear equations:


Ex 1: Solve the given equation 5x + 6 = 81

Sol:

Step 1:Given equation:   5x + 6 = 81

Step 2:Subtracting in both in 6:    5x + 6 - 6 = 81 - 6

Step 3:Simplification:      5x = 75

Ans:                   x  = 15

Ex 2 : Solve the given equation 8x + 5y = 90 and where is y = 2

Sol:

Step 1: Given equation:        8x + 5y = 90

Step 2:Substitute in y=2:   8x + 5(2) = 90

Step 3:Simplification:       8x + 10=90

8x = 90 -10

8x = 80

Ans:                x = 10

Ex 3 : Solve the given Equation: 9z + 25 = 4z + 65

Sol:

Step 1: Given equation:    9z + 25 = 4z + 65

Step 2:Subtracting both sides from 25:    9z + 25 - 25 = 4z + 65 - 25

Step 3:Simplification gives:        9z = 4z + 40

Step 4:Subtracting both sides 4z:  9z - 4z = 4z - 4z + 40

Step 5:Simplification gives:      5z = 40

Ans :    z = 8

Ex 4 :Solve 5x^2 + 2x - 3 = 0 for x.
Sol:

Step 1: Factor:   (5x - 3)(x + 1) = 0

Step 2:Simplification:   5x - 3 = 0, x + 1 = 0

Ans:  5x = 3,  x = -1

Ex 5: Solve: 4x + 9 > 97

Sol:

Step 1 Given equation:   4x + 9 > 97

Step 2  Simplification:     4x > 97 - 9,  then 4x > 88

Ans :   x > 22