Question

Form the pair of linear equations in the following problems, and find their solutions graphically. 

(i) 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz. 

(ii) 5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and that of one pen.

Answer 1

(i) Strength of the X Std. is 10 

Number of boys be ‘y’, then 

number of girls be ‘x’ . 

x + y = 10 …….. (i) 

x = y + 4 

∴ x – y = 4 ………. (ii) 

From equations (i) + (ii)

Substituting the value of ‘x’ in eqn. (i), 

x + y = 10 

7 + y = 10 

y = 10 – 7 

y = 4. 

∴ Number of girls, x = 7 

Number of boys, y = 4. 

(ii) Cost of each pencil be Rs. ‘x’ 

Cost of pen be Rs. ‘y’ 

5x + 7y = 50 ………. (i) 

7x + 5y = 46 ……….. (ii) 

From equation (i) + equation (ii)

∴ x + y = 8 …………… (iii) 

from Eqn. (ii) – Eqn. (i),

Substituting the value of ‘y’ in eqn. (i) 

x + y = 8 

x + 5 = 8 

∴ x = 8 – 5 x = 3 

∴Cost of each pencil is Rs. 3. 

Cost of each pen is Rs. 5.