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

Condition for the pair of system to have unique solution

a_{1}/a_{2} b_{1}/b_{2}

Let the equations are,

a_{1}x + b_{1}y + c_{1} = 0

and a_{2}x + b_{2}y + c_{2} = 0

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

It must satisfy the equations -

a_{1}(-1) + b_{1}(3) + c_{1} = 0

- a_{1} + 3b_{1} + c_{1} = 0 …(i)

and a_{2}(- 1) + b_{2}(3) + c_{2} = 0

- a_{2} + 3b_{2} + c_{2} = 0 …(ii)

Since for the different values of a_{1}, b_{1}, c_{1} and a_{2}, b_{2}, c_{2} satisfy the Eqs. (i) and (ii).

Hence, infinitely many pairs of linear equations are possible.

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