Question

Solve the following set of simultaneous equation.

2x + 3y + 4 = 0; x − 5y = 11

Answer 1

2x + 3y + 4 = 0    ...(I)

x − 5y = 11    ...(II)

x = 11 + 5y   ...(III)

Putting x = 11 + 5y in equation (I)

2(11 + 5y) + 3y = −4

22 + 10y + 3y = −4

22 + 13y = −4

13y = − 4 − 22

13y = −26

y = `−26/13`

y = −2

Putting y = −2 in equation (III)

x = 11 + 5 × (−2)

= 11 + (−10)

x = 1

∴ (x, y) = (1, −2)

Answer 2

2x + 3y + 4 = 0

∴ 2x + 3y = −4   ...(1)

x − 5y = 11    ...(2)

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

2x − 10y = 22     ...(3)

By subtracting equation (1) from equation (3), we get

2x − 10y = 22    ...(3)
2x + 3y = - 4      ...(1)
−    −      +    
      −13 y  = 26

  ∴ 13y = −26

∴ y = `(−26)/13`  

∴ y = −2

Substituting y = −2 in equation (2), we get

∴ x − 5y = 11

∴ x − 5(−2) = 0

∴ x + 10 = 11

∴ x = 11 − 10

∴ x = 1