# 10th cbse maths solution for exercise 3.5 part 1

This page 10th cbse maths solution for exercise 3.5 part 1is going to provide you solution for every problems that you find in the exercise no 3.5

## 10th CBSE maths solution for Exercise 3.5 part 1

(1) Which of the following pairs of linear equations has unique solution, no solution, infinitely many solutions. In case there is unique solution, find it by using cross multiplication method.

(i)   x – 3 y – 3 = 0

3 x – 9 y – 2 = 0

Solution:

From the above information let us take the values of a₁ , a₂, b₁, b₂, c₁ and c ₂

a₁ = 1          b₁ = -3             c₁ = -3

a₂ = 3         b ₂ = -9            c ₂ = -2

a₁/a₂ = 1/3

b₁/b₂ = -3/(-9) = 1/3

c₁/c₂ = -3/(-2) = 3/2

Here a₁/a₂ = b₁/b₂ ≠ c₁/c₂

From this we can decide the given lines are parallel.

(ii)  2 x +y = 5

3 x + 2 y = 8

Solution:

2 x + y – 5 = 0

3 x + 2 y – 8 = 0

From the above information let us take the values of a₁ , a₂, b₁, b₂, c₁ and c ₂

a₁ = 2         b₁ = 1            c₁ = -5

a₂ = 3         b₂ = 2            c₂ = -8

a₁/a₂ = 2/3

b₁/b₂ = 1/2

c₁/c₂ = (-5)/(-8) = 5/8

Here,a₁/a₂ ≠ b₁/b₂

Therefore two given lines are intersecting  x/(-8  + 10) = y/(-15 + 16) = 1/(4 – 3)

x/2 = y/1 = 1/1

x/2 = 1           y/1 = 1

x = 2           y = 1   10th CBSE maths solution for Exercise 3.5 part 1

(iii) 3 x – 5 y = 20

6 x – 10 y = 40

Solution:

3 x – 5 y – 20 = 0 --------(1)

6 x – 10 y – 40 = 0 --------(2)

From the above information let us take the values of a₁ , a₂, b₁, b₂, c₁ and c ₂

a₁ = 3         b₁ = -5             c₁ = -20

a₂ = 6         b₂ = -10            c₂ = -40

a₁/a₂ = 3/6 = 1/2

b₁/b₂ = -5/(-10) = 1/2

c₁/c₂ = (-20)/(-40) = 1/2

here, a₁/a₂ = b₁/b₂ = c₁/c₂

Therefore the two given lines are coincident

(iv) x – 3 y – 7 = 0

3 x – 3 y – 15 = 0

From the above information let us take the values of a₁ , a₂, b₁, b₂, c₁ and c ₂

a₁ = 1         b₁ = -3              c₁= -7

a ₂ = 3         b ₂ = -3            c ₂ = -15

a₁/a ₂ = 3/6 = 1/3

b₁/b ₂ = -3/(-3) = 1/1

c₁/c ₂ = (-7)/(-15) = 7/15

here, a₁/a ₂ ≠ b₁/b ₂

Therefore the given two lines are intersecting x/(45  - 21) = y/(-21 + 15) = 1/(-3+9)

x/24 = y/(-6) = 1/6

x/24 = 1/6           y/(-6) = 1/6

x = 24/6               y = -6/6

x = 4                       y = -1