Q6 of 62 Page 25

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

a1/a2 b1/b2


Let the equations are,


a1x + b1y + c1 = 0


and 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 Eqs. (i) and (ii).


Hence, infinitely many pairs of linear equations are possible.


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(i) 3x - y - 5 = 0 and 6x - 2y - p = 0, if the lines represented by these equations are parallel.


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