InterviewSolution
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InterviewSolution
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Write a pair of linear equations which has the unique solution x = -1 and y = 3. How many such pairs can you write ? |
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Answer» Solution :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 `a_(1)(-1)+b_(1)(3)+c_(1)=0` `rArr " " -a_(1)+3b_(1)+c_(1)=0 " " ...(i)` and `" " a_(2)(-1)+b_(2)(3)+c_(2)=0 ` `rArr " " -a_(2)+3b_(2)+c_(2)=0 " " ...(ii)` So, the different VALUES of `a_(1), a_(2), b_(1), b_(2), c_(1)` and `c_(2)` SATISFY the Eqs. (i) and (ii).  Hence, infinitely many pairs of linear equations are possible. |
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