Linear Equation in two variable.Let’s Get Started…

Edmund Halley Said…The principal use of the Analytic Art is to bring Mathematical Problems to Equations and to exhibit those Equations in the most simple terms that can be.

Edmund Halley

1) IntroductionIn earlier classes, you have studied linear equations in one variable. x + 1 = 0 and 2y + 3 = 0 are examples of linear equations in one variable. We know that such equations have a unique (i.e., one and only one) solution. The General form of linear equation in two variable is:

ax + by + C=0, in which a & b are not equal to 0, where a, b, c are being real numbers.

A solution of such a equation is a pair of values, one for x and the other for y, which makes two side of the equation equal.

Every linear equation in two variables has infinitely many solutions which can be represented on a certain line…

3) Solution of Linear Equation in two Variable

In the equation 2x+3y=18 determine if the ordered pair (3,4) is a solution to the equation. We substitute 3 in x and 4 in y. 2x+3y=18

2(3)+3(4)=18

6+12=18

18=18

2) Writing in standard FormWriting the equations in the form of ax + by + c=0 and indicating the values of a, b and c.

(i) 2x + 3y=4.37

2x + 3y – 4.37=0

a=2, b=3, c=-4.37

Let us consider the following equation. (i) 2x-y=-1

Here we assign any value to one of the two variables and then determine the value of the other variable from the given equation.

4) Graphical Solution of Linear equation in two variable

x 0 1 2

y 1 3 5

if x=0 2(0)-y=-1 -y=-1 y=1. if x=1 2(1)-y=-1 2-y=-1 -y=-1-2, y=3if x=2 2(2)-y=-1 4-y=-1 -y=-1-4, y=5

Y

Y’

X X’ 1

2

3

4

5

-1

-2

1

2 3 4 5-1-2-3-4-5

(0,1)

(1,3)

(2,5)

IX-BRoll No: 33

Mohd.Imran