Question

The pair of equations x + 2y + 5 = 0 and – 3x – 6y + 1 = 0 have,
A) a unique solution B) exactly two solutions
C) infinitely many solutions D) no solutions

Answer 1

Answer:

option (D) NO SOLUTION

Answer 2

Given:

The pair of equations:

x + 2y + 5 = 0 and – 3x – 6y + 1 = 0

To Find:

The no. of solutions of pair of equations.

Solution:

Two equation has,

Uniques solution : a₁/a₂ ≠ b₁/b₂

No solution:  a₁/a₂ = b₁/b₂ ≠ c₁/c₂

Infinite many solution:  a₁/a₂ = b₁/b₂ = c₁/c₂

Given equations are:

x + 2y + 5 = 0 and – 3x – 6y + 1 = 0

a₁ = 1                    a₂ = -3

b₁ = 2                   b₂ = -6

c₁ = 5                    c₂ = 1

so,

a₁/a₂= 1/-3= -1/3

b₁/b₂ = 2/-6 = -1/3

c₁/c₂ = 5/1

∴ a₁/a₂ = b₁/b₂ ≠ c₁/c₂ ,

this condition is satisfied

Hence, the pair of equations x + 2y + 5 = 0 and – 3x – 6y + 1 = 0 have no solution.