Chapter 4 linear Equation In Two Variables

• The solution of a linear equation does not change if.

(i) The same number is added or subtracted from both sides of the equation.

(ii) We multiply or divide both sides of equation by the same number.

• Any equation which can be in the form

ax + by + c = 0 where a, b , c are real numbers

a¹ 0, b ¹ 0,  is called a Linear.Equation in two variables

• A Linear.Equation can have many solutions

Exercise 4.1

• The cost of a notebook is twice the cost of pen. Write a linear equation in two variables to represent this statement.

(Take the cost of a notebook to be  D  x and that of pen to be D  y)

Solution

Let the cost of the notebook be ‘x’

And the cost of the pen be ‘y’

(Notebook)=2(Pen) as per the question

x = 2y

\x – 2y=0 is the required Linear.Equation

• Express the following linear equations in the form ax + by + c = 0 and indicate the value of a, b and c in each case:

Solution

(i)         2x+3y=9.35

\2x=3y-9.35=0

2(x)+3(y)+(-9.35)=0

Comparing with   ax+by+c=0

We get

a=2 ,b=3 and c=-9.35

(ii)        x-  -10=0

\1(x)+(- )y=(-10)=0.

Comparing with   ax+by+c=0   we get

a= 1, b= –   c= -10

(iii)       -2x+3y-6-0

-2y + 3y – 6 = 0

(-2)x+(3)y+(-6)=0

Comparing with   ax+by+c=0   we get

a=-2 , b=3 , c=-6

(iv)       x=3y.

X – 3y=0

\1(x)+(-3)y+0=0

Comparing with   ax+by+c=0  we get

A=1 , b=-3 , c=0.

(v)        2x= -5y

2x-5y=0

\(2)x+(-5)y+0=0

Comparing with    ax+by+c=0     we get

a-2 , b= -5 , c=0

(vi)       3x+2=0

(3)x+(0)y+2=0.

Comparing with   ax+by+c=0   we get

a=3 , b=0 , c=2

(vii)      y-2=0

(0)x+1(y)+(-2)=0

Comparing with    ax+by+c=0    we get

a=0 , b=1 , c= -2

(viii)     5=2x

5-2x=0

(-2)x+0(y)+5=0

Comparing with  ax+by+c=0   we get

a= -2 , b=0 and c=5.