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| 1. |
Find the value of k for which system of eq. X-2y=3 and3x+ky=1 has a unique solution |
| Answer» The given system of equations isx - 2y - 3 = 0 .................... (i)3x + ky - 1 = 0 ................ (ii)These equations are of the forma1x + b1y+ c1\xa0= 0 ........ (iii)a2x + b2y +c2= 0 ........ (iv)Compare (i) and (iii) and (ii) and (iv), we geta1 = 1, b1= -2, c1= -3\xa0and a2\xa0= 3, b2\xa0= k, c2= -1For a unique solution, we must have\xa0{tex}\\frac { a _ { 1 } } { a _ { 2 } } \\neq \\frac { b _ { 1 } } { b _ { 2 } }{/tex}{tex}\\therefore \\quad \\frac { 1 } { 3 } \\neq \\frac { - 2 } { k } \\Rightarrow k \\neq - 6{/tex}Hence, the given system of equations will have a unique solution for all real values of k, other than - 6. | |