By equating coefficients of variables, i. 3x – 4y = 7 ; 5x + 2y = 3 ii. 5x + 7y= 17 ; 3x – 2y = 4

Question

By equating coefficients of variables, solve the following equations.

i. 3x – 4y = 7 ; 5x + 2y = 3 

ii. 5x + 7y= 17 ; 3x – 2y = 4

Answer 1

i. 3x – 4y = 7 …(i)

 5x + 2y = 3 ….(ii)

Multiplying equation (ii) by 2, 

10x + 4y = 6 …(iii) 

Adding equations (i) and (iii),

∴ x = 1 

Substituting x = 1 in equation (i), 

3x – 4y = 7 

∴ 3(1) – 4y = 7 

∴ 3 – 4y = 7 

∴ 3 – 7 = 4y 

∴ -4 = 4y 

∴ y = 

∴ y = -1 

∴ (1, -1) is the solution of the given equations.

ii. 5x + 7y = 17 …(i) 

3x – 2y = 4 ….(ii)

 Multiplying equation (i) by 2,

10x + 14y = 34 …(iii) 

Multiplying equation (ii) by 7,

 21x – 14y = 28 …..(iv) 

Adding equations (iii) and (iv),

∴ x = 2 

Substituting x = 2 in equation (ii), 

3x – 2y = 4 

∴ 3(2) – 2y = 4 

∴ 6 – 2y = 4 

∴ 6 – 4 = 2y 

∴ 2 = 2y 

∴ y = 

∴ y = 1 

∴ (2,1) is the solution of the given equations.