Question

Solve the following set of simultaneous equation. 

2x + y = 5; 3x - y = 5

Answer 1

2x + y = 5               

∴ y = 5 - 2x   ...(I)

3x - y = 5   ...(II)

Substituting (I) in (II)

3x - y = 5

∴  3x - (5 - 2x) = 5

∴ 3x - 5 + 2x = 5

∴ 5x = 5 + 5

5x = 10

⇒ `x = 10/5 = 2`                         

Putting x = 2 in (I) we have,

2 × 2 + y = 5

⇒ 4 + y = 5

⇒ y = 1

(x, y) = (2, 1)

Answer 2

2x + y = 5   ...(1)

3x - y = 5    ...(2)

By adding equations (1) and (2),

2x + y = 5       ...(1)
3x - y =  5       ...(2)
5x  = 10

∴ x = `10/5`

∴ x = 2

Substituting x = 2 in equation (1), we get

∴ 2x + y = 5 

∴ 2(2) + y = 5

∴ 4 + y = 5

∴ y = 5 - 4

∴ y = 1