## EXERCISE 3.3

#### Page No 53:

#### Question 1:

Solve the following pair of linear equations by the substitution method.

#### Answer:

(i)* x* + *y* = 14 (1)

*x* − *y* = 4 (2)

From (1), we obtain

*x* = 14 − *y* (3)

Substituting this value in equation (2), we obtain

Substituting this in equation (3), we obtain

(ii)** **

From (1), we obtain

Substituting this value in equation (2), we obtain

Substituting in equation (3), we obtain

*s* = 9

*s* = 9, *t* = 6

(iii)3*x* − *y* = 3 (1)

9*x* − 3*y* = 9 (2)

From (1), we obtain

*y* = 3*x* − 3 (3)

Substituting this value in equation (2), we obtain

9 = 9

This is always true.

Hence, the given pair of equations has infinite possible solutions and the relation between these variables can be given by

*y* = 3*x* − 3

Therefore, one of its possible solutions is *x* = 1, *y* = 0.

(iv)** **

From equation (1), we obtain

Substituting this value in equation (2), we obtain

Substituting this value in equation (3), we obtain

(v)** **

From equation (1), we obtain

Substituting this value in equation (2), we obtain

Substituting this value in equation (3), we obtain

*x* = 0

*x* = 0, *y* = 0

(vi)** **

From equation (1), we obtain

Substituting this value in equation (2), we obtain

Substituting this value in equation (3), we obtain

Hence, *x* = 2, *y* = 3

Video Solution

#### Question 2:

Solve 2*x* + 3*y* = 11 and 2*x *− 4*y* = − 24 and hence find the value of ‘*m*’ for which *y* = *mx* + 3.

#### Answer:

From equation (1), we obtain

Substituting this value in equation (2), we obtain

Putting this value in equation (3), we obtain

Hence, *x* = −2, *y* = 5

Also,

Video Solution

#### Question 3:

#### Answer:

(i) Let the first number be *x* and the other number be *y* such that *y* > *x*.

According to the given information,

On substituting the value of *y* from equation (1) into equation (2), we obtain

Substituting this in equation (1), we obtain

*y* = 39

Hence, the numbers are 13 and 39.

(ii) Let the larger angle be *x* and smaller angle be *y*.

We know that the sum of the measures of angles of a supplementary pair is always 180º.

According to the given information,

From (1), we obtain

*x* = 180º − *y* (3)

Substituting this in equation (2), we obtain

Putting this in equation (3), we obtain

*x* = 180º − 81º

= 99º

Hence, the angles are 99º and 81º.

(iii) Let the cost of a bat and a ball be *x* and *y* respectively.

According to the given information,

From (1), we obtain

Substituting this value in equation (2), we obtain

Substituting this in equation (3), we obtain

Hence, the cost of a bat is Rs 500 and that of a ball is Rs 50.

(iv) Let the fixed charge be Rs *x *and per km charge be Rs *y*.

According to the given information,

From (1), we obtain

Substituting this in equation (2), we obtain

Putting this in equation (3), we obtain

Hence, fixed charge = Rs 5

And per km charge = Rs 10

Charge for 25 km = *x* + 25*y*

= 5 + 250 = Rs 255

(v) Let the fraction be .

According to the given information,

From equation (1), we obtain

Substituting this in equation (2), we obtain

Substituting this in equation (3), we obtain

Hence, the fraction is .

(vi) Let the age of Jacob be *x *and the age of his son be *y*.

According to the given information,

From (1), we obtain

Substituting this value in equation (2), we obtain

Substituting this value in equation (3), we obtain

Hence, the present age of Jacob is 40 years whereas the present age of his son is 10 years.