Question

Write a pair of linear equations which has the unique solution x = – 1, y = 3. How many such pairs can you write?

Answer 1

Condition for the pair of system to have unique solution

`a_1/a_2 ≠ b_1/b_2`

Let the equations be,

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂ = 0

Since, x = – 1 and y = 3 is the unique solution of these two equations, then

It must satisfy the equations 

a₁(–1) + b₁(3) + c₁ = 0

– a₁ + 3b₁ + c₁ = 0   ......(i)

and a₂(–1) + b₂(3) + c₂ = 0

– a₂ + 3b₂ + c₂ = 0   .......(ii)

Since for the different values of a₁, b₁, c₁ and a₂, b₂, c₂ satisfy the equations (i) and (ii).

Hence, infinitely many pairs of linear equations are possible.