NCERT solutions for class 10 maths chapter 3 part 2

In this page NCERT solutions for class 10 maths chapter 3 part 2 you can find solutions for exercise problems.

NCERT solutions for class 10 maths chapter 3 part 2

(2) On comparing the ratios a₁/a₂, b₁/b₂ and  c₁/c₂, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.

(i)  5 x – 4 y + 8 = 0

     7 x + 6 y – 9 = 0

Solution:

From the above information let us take the values of a₁, a₂, b₁, b₂, c₁ and c₂

 a₁ = 5         b₁ = -4             c₁ = 8

 a₂ = 7          b₂ = 6             c₂ = -9

a₁/a₂ = 5/7

b₁/b₂ = -4/6

c₁/c₂ = -8/9

Here a₁/a₂ ≠ b₁/b₂

From this we can decide that these two lines are intersecting.

(ii)  9 x + 3 y + 12 = 0

      18 x + 6 y + 24 = 0

Solution:

From the above information let us take the values of a₁, a₂, b₁, b₂, c₁ and c₂

 a₁ = 9           b₁ = 3             c₁ = 12

 a₂ = 18         b₂ = 6            c₂ = 24

a₁/a₂ = 9/18 = 1/2

b₁/b₂ = 3/6 = 1/2

c₁/c₂ = 12/24 = 1/2

Here a₁/a₂ = b₁/b₂= c₁/c₂

From this we can decide that the given two lines are coincident.

(iii)  6 x - 3 y + 10 = 0

        2 x - y + 9 = 0         

Solution:

From the above information let us take the values of a₁, a₂, b₁, b₂, c₁ and c₂

 a₁ = 6          b₁ = -3            c₁ = 10

 a₂ = 2         b₂ = - 1           c₂ = 9

a₁/a₂ = 6/2 = 3

b₁/b₂ = -3/-1 =  3

c₁/c₂ = 10/9

Here a₁/a₂ = b₁/b₂ ≠ c₁/c₂

From this we can decide that the given two lines are parallel.

(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.

(i) 3 x + 2 y = 5

     2 x - 3 y = 7

(ii) 2 x - 3 y = 8

     4 x - 6 y = 9

(iii) (3/2) x + (5/3) y = 7

      9 x - 10 y = 14

(iv) 5 x -3 y = 7

      9 x - 10 y = 14

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

      2 x + 3 y = 12

Solution

Go to Exercise 3.2




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