Question

The pair of linear equations x = y and x + y = 0 has
(a)no common solution
(b) infinitely many solution
(c) unique solution
(d) inconsistent

Answer 1

I think unique solution.

hope it helps you....

Answer 2

Given:

The pair of linear equations x = y and x + y = 0

To Find:

No.of solutions of pair of linear equations.

Solution:

a₁x+ b₁y + c₁ = 0   and    a₂x+ b₂y + c₂ = 0

this pair of equation  will have,

unique solution -  a₁/a₂ ≠ b₁/b₂

no solution -- a₁/a₂ = b₁/b₂ ≠ c₁/c₂

infinite solution --  a₁/a₂ = b₁/b₂ = c₁/c₂

The pair of linear equations x = y and x + y = 0

it can written as,

x - y = 0          x + y = 0

a₁ = 1              a₂ = 1

b₁ = -1               b₂ = 1

as,

 a₁/a₂ = 1

b₁/b₂  = -1

∴   a₁/a₂ ≠ b₁/b₂

Hence, the pair of linear equations unique solution.