chapter-3 exercise 3.1-Q3-pair of linear equations in two variables

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Q 3. On comparing the ratios a1/a2, b1/b2 and c1/c2, find out whether the following pair of linear equations are    consistent, or inconsistent.

Solutions: 

(i) 3x + 2y = 5 ; 2x – 3y = 7 

First make linear equation form

3x + 2y – 5 = 0 

2x – 3y – 7 = 0

Now make ratio form

a1/a2=3/2, b1/b2=2/-3 

c1/c2=-5/-7

from the above we can say

a1/a2 ≠ b1/b2

this formula belongs to Intersect point lines

Intersect lines are consistent


 (ii) 2x – 3y = 8 ; 4x – 6y = 9

First make linear equation form

2x – 3y - 8 = 0  

4x – 6y - 9 = 0

Now make ratio form

a1/a2=2/4=1/2, b1/b2=-3/-6=1/2 

c1/c2=-8/-9

from the above we can say

a1/a2 = b1/b2 ≠ c1/c2

this formula belongs to parallel lines

parallel lines are inconsistent


(iii) 3/2x + 5/3y = 7 ; 9x – 10y = 14 

First make linear equation form

3/2x + 5/3y - 7 = 0  

9x – 10y - 14 = 0

Now make ratio form

a1/a2 = 3/2/9/1=3/18=1/6, 

b1/b2 = 5/3/-10/1 = 5/-30 = -1/6 

c1/c2=-7/-14 = 1/2

from the above we can say

a1/a2 ≠  b1/b2

this formula belongs to intersect at point lines

Intersect at point lines are consistent


(iv) 5x – 3y = 11 ; – 10x + 6y = –22

First make linear equation form

5x – 3y – 11 = 0 

– 10x + 6y + 22 = 0

Now make ratio form

a1/a2 = 5/-10 = -1/2, b1/b2 = -3/6 = -1/2 

c1/c2 = -11/22 = -1/2

from the above we can say

a1/a2 = b1/b2 = c1/c2

this formula belongs to coincident lines

coincident lines are consistent


(v) 4/3x + 2y = 8 ; 2x + 3y = 12

First make linear equation form

4/3x + 2y - 8 = 0  

2x + 3y - 12 = 0

Now make ratio form

a1/a2 = 4/3/2/1 = 4/6 = 2/3, 

b1/b2 = 2/3,

c1/c2 = -8/-12 = 2/3

from the above we can say

a1/a2 = b1/b2  = c1/c2

this formula belongs to coincident lines

coincident lines are consistent


Post details

cbse class 10 maths (ncert 10 maths) solutions

chapter : pair of linear equations in two variables

chapter 3

exercise 3.1

question no.3

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