LINEAR EQUATION IN TWO VARIABLE

THIS IS TO CERTIFY THAT MATHS PRESENTATION IS MADE BY Mr. RAJAN

PANCHAL ACCORDING TO OUR SYLLABUS

Maths

ism

y

favou

rite

subje

ct

I love

maths

LINEAR EQUATION IN TWO VARIABLE

Ax+By=c

• LINEAR EQUATION• FORM OF LINEAR EQUATION• TYPES OF LINEAR EQUATION• GRAPH OF A EQUATION• TYPES OF GRAPH• HOW CAN KNOW ABOUT GRAPH?• EXAMPLES OF TYPES OF GRAPH• FORMULA OF CROSS – MULTIPLICATION• SOLVE QUESTION

LINEAR EQUATION

Linear equations are functions which have two variables. They have an independent and dependent variable.

Independent Variables

Independent variables are variables that you put into the equations

Dependent Variables

Dependent variables are variables that you solve for

The general form for a pair of linear equation in two variables of x and y is ->

a1 + b1 +c1 = 0

a2 + b2 + c2 = 0

Where a1,b1,c1,a2,b2,c2 are real numbers and a, and b both are not zero.

What is linear equation in two variable?Equations of the form ax + by = c are called linear

equations in two variables.

How many types of method to find the solution of pair of linear equation?

There are of four types

1. Elimination method

2. Substitution method

3. Cross-multiplication method

4. Graph method

Linear equation graph

x

y

2-2

This is the graph of the equation 2x + 3y = 12.

The point (0,4) is the y-intercept.

The point (6,0) is the x-intercept.

The graph of a pair of variable is represnted by two lines

• If the line intersect at a point, then that point gives a unique solution and the pair of equation is consistent.

• If the line is coincide, then there are infinite many solution and the pair of equation is consistent

• If the line are parallel, then there are no solution and the pair of equation is inconsistent.

a1 ≠ b1 so the pair of linear equation is unique.

a2 b2

a1=b1 ≠c1 so the pair of linear equation is no

a2 b2 c2 solution.

a1=b1= c1 so the pair of linear equation is infinity

a2 b2 c2 many solution

If a1=b1 ≠c1 so the lines will be parallel. a2 b2 c2

Example: The lines 2x – y = 3 and 2x –y = -4

2 = -1 ≠ 3

2 -1 -4

(0, 4)

(0, -3)

Two lines are parallel if

The lines are parallel.

Two lines are coincident if

If a1=b1 =c1 so the lines will be coincident.

a2 b2 c2

Example: The lines 9x + 3y = -12and18x + 6y = -24

9 = 3 ≠ -12

18 6 -24

The lines are coincident.

(-2,2)

0,-4)

(-1,-1)

.

Two lines are intersect if

Example: The lines 2x + y = 5and 2x –2y = 2

2 ≠ 1

2 -2

The lines are Intersect.

If a1=b1 =c1 so the lines will be intersect.

a2 b2 c2(0,5)

(0,1)

(2,1)

How to solve equation by cross multiplication method?

Method to solve equation by cross multiplication in linear equation in two variable.

x = b1c2 – c1b2

a1b2 – b1a2 y = c1a2 – a1c2

a1b2 – b1a2