Question

Solve the following set of simultaneous equation.

x + y = 4 ; 2x - 5y = 1

Answer 1

x + y = 4      ...(I)

2x - 5y = 1   ...(II)

From (I) we have

x = 4 - y

Putting this value of x in (II)

2 (4 - y) - 5y = 1

⇒ 8 - 2y - 5y = 1

⇒ 8 - 7y = 1

⇒ 8 - 1 = 7y

⇒ 7 = 7y

⇒ y = 1

Putting the value of y in (I) we have

x + 1 = 4

⇒ x = 3

Thus, (x, y) = (3, 1)

Answer 2

x + y = 4      ...(i)

2x - 5y = 1   ...(ii)

On multiplying both sides of equation (i) by 5,

5x + 5y = 20    ...(iii)

By adding equations (ii) and (iii),

5x + 5y = 20    ...(iii)
2x - 5y = 1       ...(ii)
7x  = 21

∴ x = `21/7`

∴ x = 3

Substituting x = 3 in equation (i), we get

∴ x + y = 4

∴ 3 + y = 4

∴ y = 4 - 3

∴ y = 1