InterviewSolution
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InterviewSolution
| 1. |
Find the value of \'k\' for the following equation has a unique solution:4x -5y=k, 2x-3y=12 |
| Answer» The given equations are4x - 5y = k\xa0So, 4x - 5y - k = 0......... (i)And 2x - 3y = 12So, 2x - 3y - 12 = 0 ......... (ii)The system of linear equations is in the form ofa1x + b1y + c1\xa0= 0a2x + b2y + c2\xa0= 0Compare (i) and (ii), we geta1= 4\xa0,b1= -5, c1\xa0= -k,a2=2\xa0,b2= -3\xa0,c2\xa0= -12For a unique solution, we must have{tex} \\frac { a _ { 1 } } { a _ { 2 } } \\neq \\frac { b _ { 1 } } { b _ { 2 } }{/tex}{tex}\\frac { 4 } { 2 } \\neq \\frac { - 5 } { - 3 }{/tex}{tex}2 \\neq \\frac { 5 } { 3 } \\Rightarrow 6 \\neq 5{/tex}Thus, for all real value of k, the given system of equations will have a unique solution. | |