Find the value of c in …
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Sia ? 6 years, 7 months ago
cx + 3y + ( 3 - c ) = 0 and 12x + cy - c = 0
Condition 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 = c, b1 = 3, c1 = 3 - c
and a2 = 12, b2 = c, c2 = -c
Putting 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 = 36
{tex}c = \pm \sqrt { 36 }{/tex}
c = ± 6
here c = -6 is rejected as it does not satisfy the 2nd equality.
Therefore, c = 6
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