By equating coefficients of variables, i. x – 2y = -10 ; 3x – 3y = -12 ii. 4x + y = 34 ; x + 4y = 16

Question

By equating coefficients of variables, solve the following equations.

i. x – 2y = -10 ; 3x – 3y = -12 

ii. 4x + y = 34 ; x + 4y = 16

Answer 1

i. x – 2y = -10 ….(i) 

3x – 5y = -12 …….(ii)

Multiplying equation (i) by 3, 

3x – 6y = -30 …(iii) 

Subtracting equation (ii) from (iii),

∴ y = 18 

Substituting y = 18 in equation (i),

 x – 2y = -10

∴ x – 2(18) = -10

∴ x – 36 = -10 

∴ x = -10 + 36 = 26 

∴ (26, 18) is the solution of the given equations.

ii. 4x + y = 34 …(i) 

x + 4y = 16 …… (ii) 

Multiplying equation (i) by 4, 

16x + 4y = 136 …(iii) 

Subtracting equation (ii) from (iii),

x = 8 

Substituting x = 8 in equation (i), 

4x + y = 34 

∴ 4(8) + y = 34 

∴ 32 + y = 34 

∴ y = 34 – 32 = 2 

∴ (8, 2) is the solution of the given equations.