3x-y-5=06x-2y-p=0Find p when given lines are parellel

1.	3x-y-5=06x-2y-p=0Find p when given lines are parellel
Answer» The given equations are3x - y - 5 = 0 ......... (i)6x - 2y + k = 0 .......... (ii)The system of linear equations\xa0a1x + b1y + c1\xa0= 0a2x + b2y + c2\xa0= 0Compare (i) and (ii), we geta1 = 3, b1 = -1, c1 = -5and a2 = 6, b2 = -2 , c2 = kThe equations has no solution if\xa0{tex}\\frac { a _ { 1 } } { a _ { 2 } } = \\frac { b _ { 1 } } { b _ { 2 } } \\neq \\frac { c _ { 1 } } { c _ { 2 } }{/tex}{tex}\\Rightarrow \\frac { 3 } { 6 } = \\frac { - 1 } { - 2 } \\neq \\frac { - 5 } { k }{/tex}So,{tex}- \\mathrm { k } \\neq 10{/tex}{tex} \\Rightarrow \\mathrm { k } \\neq - 10{/tex}

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