Question

Solve the following set of simultaneous equation.

2x - 7y = 7; 3x + y = 22

Answer 1

2x − 7y = 7   ...(I)

3x + y = 22     ...(II)

y = 22 − 3x    ...(III)

Putting y = 22 − 3x in equation (I)

2x − 7(22 − 3x) = 7

2x − 154 + 21x = 7  

23x = 7 + 154

23x = 161

x = `161/23`

x = 7

Putting x = 7 in equation (III)

y = 22 − 3 × 7

y = 22 − 21

y = 1

∴ (x, y) = (7, 1)

Answer 2

2x − 7y = 7     ...(1)

3x + y = 22     ...(2)

On multiplying both sides of equation (2) by 7, we get

21x + 7y = 154        ...(3)

By adding equations (1) and (3),

21x + 7y = 154    ...(3)
2x − 7y = 7          ...(1)
 23 x  = 161

 ∴ x = `(161)/23`  

∴ x = 7

Substituting x = 7 in equation (2), we get

∴ 3x + y = 22

∴ 3(7) + y = 22

∴ 21 + y = 22

∴ y = 22 − 21

∴ y = 1