## RS Aggarwal Class 10 Solutions Chapter 3 Linear equations in two variables MCQS

These Solutions are part of RS Aggarwal Solutions Class 10. Here we have given RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables MCQS.

### RS Aggarwal Solutions Class 10 Chapter 3

**Choose the correct answer in each of the following questions.****Question 1.****Solution:****(c)**

**Question 2.****Solution:****(c)**

**Question 3.****Solution:****(a)**

**Question 4.****Solution:****(d)**

**Question 5.****Solution:****(a)**

**Question 6.****Solution:****(b)**

**Question 7.****Solution:****(c)** 4x + 6y = 3xy, 8x + 9y = 5xy

Dividing each term by xy,

**Question 8.****Solution:****(a)**

**Question 9.****Solution:****(c)**

**Question 10.****Solution:****(b)**

**Question 11.****Solution:****(d)**

**Question 12.****Solution:****(b)**

**Question 13.****Solution:****(a)**

**Question 14.****Solution:****(d)**

**Question 15.****Solution:****(d)**

**Question 16.****Solution:****(d)**

**Question 17.****Solution:****(d)**

**Question 18.****Solution:****(d)** The system of equations is consistent then their graph lines will be either intersecting or coincident.

**Question 19.****Solution:****(a)** The pair of lines of equation is inconsistent then the system will not have no solution i.e., their lines will be parallel.

**Question 20.****Solution:****(b)**

**Question 21.****Solution:****(b)** ABCD is a cyclic quadrilateral

∠A = (x + y + 10)°, ∠B = (y + 20)°, ∠C = (x + y – 30)° and ∠D = (x + y)°

∠A + ∠C = 180°

Now, x + y + 10°+ x + y – 30° = 180°

⇒ 2x + 2y – 20 = 180°

⇒ 2x + 2y = 180° + 20° = 200°

⇒ x + y = 100° …(i)

and ∠B + ∠D = 180°

⇒ y + 20° + x + y = 180°

⇒ x + 2y = 180° – 20° = 160° …(ii)

Subtracting,

-y = -60° ⇒ y = 60°

and x + 60° = 100°

⇒ x = 100° – 60° = 40°

Now, ∠B = y + 20° = 60° + 20° = 80°

**Question 22.****Solution:****(d)** Let one’s digit of a two digit number = x

and ten’s digit = y

Number = x + 10y

By interchanging the digits,

One’s digit = y

and ten’s digit = x

Number = y + 10x

According to the conditions,

x + y = 15 …(i)

y + 10x = x + 10y + 9

⇒ y + 10x – x – 10y = 9

⇒ 9x – 9y = 9

⇒ x – y = 1 …(ii)

Adding (i) and (ii),

2x = 16 ⇒ x = 8

and x + y = 15

⇒ 8 + y = 15

⇒ y = 15 – 8 = 7

Number = x + 10y = 8 + 10 x 7 = 8 + 70 = 78

**Question 23.****Solution:****(b)** Let the numerator of a fractions = x

and denominator = y

**Question 24.****Solution:****(d)** Let present age of man = x years

and age of his son = y years

5 years hence,

Age of man = (x + 5) years

and age of son = y + 5 years

(x + 5) = 3 (y + 5)

⇒ x + 5 = 3y + 15

x = 3y + 15 – 5

x = 3y + 10 ……(i)

and 5 years earlier

Age of man = x – 5 years

and age of son = y – 5 years

x – 5 = 7 (y – 5)

x – 5 = 7y – 35

⇒ x = 7y – 35 + 5

x = 7y – 30 ……….(ii)

From (i) and (ii),

7y – 30 = 3y + 10

⇒ 7y – 3y = 10 + 30

⇒ 4y = 40

y = 10

x = 3y + 10 = 3 x 10 + 10 = 30 + 10 = 40

Present age of father = 40 years

**Question 25.****Solution:****(b)**

**Question 26.****Solution:****(c)**

**Question 27.****Solution:****(a)**

The system has infinitely many solutions.

The lines are coincident.

Hope given RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables MCQS are helpful to complete your math homework.

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