Question

Solve the following simultaneous equations.

i. 2x + y = 5 ; 3x – y = 5 

ii. x – 2y = -1 ; 2x – y = 7 

Answer 1

i. 2x + y = 5 …(i) 

3x – y = 5 …(ii)

 Adding equations (i) and (ii), 

2x + y = 5 

3x – y = 5 

5x = 10 

∴ x = 10/5 

∴ x = 2 

Substituting x = 2 in equation (i),

 2(2) + y = 5

 4 + y = 5 

∴ y = 5 – 4 = 1 

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

ii. x – 2y = -1 

∴x = 2y – 1 … .(i) 

∴ 2x – y = 7 ….(ii)

 Substituting x = 2y – 1 in equation (ii), 

2(2y – 1) – y = 7 

∴ 4y – 2 – y = 7 

∴ 3y = 7 + 2

∴ 3y = 9 

∴ y = 9/3 

∴ y = 3 

Substituting y = 3 in equation (i),

 x = 2y – 1 

∴ x = 2(3) – 1

 ∴ x = 6 – 1 = 5 

∴ (5, 3) is the solution of the given equations.