NCERT solutions for class 10 maths chapter 3 part 3

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

NCERT solutions for class 10 maths chapter 3 part 3

(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

Solution:

    3 x + 2 y – 5 = 0

     2 x - 3 y - 7 = 0

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

 a₁ = 3          b₁ = 2            c₁ = -5

 a₂ = 2         b₂ = - 3           c₂ = -7

a₁/a₂ = 3/2

b₁/b₂ = 2/3

c₁/c₂ = -5/-7 = 5/7

This exactly matches the condition a₁/a₂≠ b₁/b₂.

From this we can decide the two lines are intersecting. So  it is consistent.


(ii) 2 x - 3 y = 8

     4 x - 6 y = 9

Solution:

     2 x - 3 y – 8 = 0

     4 x - 6 y -9 = 0

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

 a₁ = 2          b₁ = -3            c₁ = -8

 a₂ = 4         b₂ = -6            c₂ = -9

a₁/a₂ = 2/4 = 1/2

b₁/b₂ = -3/-6 = 1/2

c₁/c₂ = -8/-9 = 8/9

This exactly matches the condition a₁/a₂ = b₁/b₂ ≠ c₁/c₂

From this we can decide the two lines are parallel. It means these two lines will not intersect each other.

So it is inconsistent.


(iii)  (3/2) x + (5/3) y = 7

       9 x - 10 y = 14

Solution:

     (3/2) x + (5/3) y – 7 = 0

    9 x - 10 y – 14 = 0

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

 a₁ = 3/2          b₁ = 5/3            c₁ = -7

 a₂ = 9             b₂= -10            c₂ = -14

a₁/a₂ = (3/2)/9 = 1/6

b₁/b₂ = (5/3)/-10 =- 1/6

c₁/c₂ = -7/-14 = 1/2

This exactly matches the condition a₁/a₂ ≠ b₁/b₂

From this we can decide the two lines are intersecting. So it is consistent.


(iv) 5 x -3 y = 7

      9 x - 10 y = 14

Solution:

     (3/2) x + (5/3) y – 7 = 0

    9 x - 10 y – 14 = 0

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

 a₁ = 3/2          b₁ = 5/3            c₁ = -7

 a₂ = 9              b₂ = -10            c₂ = -14

a₁/a₂ = (3/2)/9 = 1/6

b₁/b₂ = (5/3)/-10 =- 1/6

c₁/c₂ = -7/-14 = 1/2

This exactly matches the condition a₁/a₂ ≠ b₁/b₂

From this we can decide the two lines are intersecting. So it is consistent.


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

      2 x + 3 y = 12

Solution:

     (4/3) x + 2 y – 8 = 0

   2 x + 3 y – 12 = 0

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

 a₁ = 4/3          b₁ = 2            c₁ = -8

 a₂ = 2             b₂ = 3            c₂ = -12

a₁/a₂ = (4/3)/2 = 2/3

b₁/b₂ = 2/3

c₁/c₂ = -8/-12 = 2/3

This exactly matches the condition a₁/a₂ = b₁/b₂ = c₁/c₂

From this we may decide the two lines are coincident. So it is consistent.

Go to Exercise 3.2




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