Question

Solve the following set of simultaneous equations.

2y − x = 0; 10x + 15y = 105

Answer 1

2y − x = 0

2y = x

∴ x = 2y    ...(I)

10x + 15y = 105     ...(II)

Putting x = 2y in equation (II)

10 × 2y + 15y = 105

20y + 15y = 105

35y = 105

y = `105/35`

∴ y = 3

Putting y = 3 in equation (I)

x = 2 × 3 = 6

∴ (x, y) = (6, 3)

Answer 2

2y − x = 0   

∴ − x + 2y = 0   

∴ x − 2y = 0     ...(1)   ...[Multiplying both sides by −1]

10x + 15y = 105   

∴ 2x + 3y = 21     ...(2)   ...[division by 5 on both sides]

On multiplying both sides of equation (1) by 2, we get

2x − 4y = 0      ...(3)

By subtracting equation (3) from equation (2), we get

2x + 3y = 21    ...(2)
2x − 4y =  0     ...(3)
−      +               
      7y  = 21

  ∴ y = `21/7`

  ∴ y = 3

Substituting y = 3 in equation (1), we get

∴ x − 2y = 0

∴ x − 2(3) = 0

∴ x − 6 = 0

∴ x = 6