Find the value of c in the eq.systemcx+3y+(3-c)=0 eq.112x+cy-c=0 eq.2

1.	Find the value of c in the eq.systemcx+3y+(3-c)=0 eq.112x+cy-c=0 eq.2
Answer» cx + 3y + ( 3 - c ) = 0 and 12x +\xa0cy - c = 0Condition for infintely many solutions,{tex}\\frac { a _ { 1 } } { a _ { 2 } } = \\frac { b _ { 1 } } { b _ { 2 } } = \\frac { c _ { 1 } } { c _ { 2 } }{/tex}From given system of equation,a1\xa0= c, b1\xa0= 3, c1\xa0= 3 - cand a2\xa0= 12, b2\xa0= c, c2\xa0= -cPutting these values in condition,we get{tex}\\frac { c } { 12 } = \\frac { 3 } { c } = \\frac { 3 - c } { - c }{/tex}Considering first equality, i.e{tex}\\frac { c } { 12 } = \\frac { 3 } { c }{/tex}{tex}( c ) \\times ( c ) = 3 \\times 12{/tex}c2\xa0= 36{tex}c = \\pm \\sqrt { 36 }{/tex}c = ± 6here c = -6 is rejected as it does not satisfy the 2nd equality.Therefore, c = 6

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