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

(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.

**Solution for exercise 3.2 (part 1)****Solution for exercise 3.2 (part 2)****Solution for exercise 3.2 (part 4)****Solution for exercise 3.2 (part 5)**

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