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  • Find  if the system of equations <img alt="cx+3y+(3-c)=0;\: 12x+cy-c=0" src="https://entrancecorner.codecogs.com/gif.latex?cx&plus;3y&plus;%283-c%29%3D0%3B%5C%3A%201

Find c if the system of equations cx+3y+(3-c)=0;\: 12x+cy-c=0  has infinitely many solutions?

 

 

Answers (1)

Given,

cx+3y+(3-c)=0\: \: \: \: -(1);\: 12x+cy-c=0\: \: \: \: -(2)in two equations, a_1x+b_1y+c_1=0\: \: and\: \: a_2x+b_2y+c_2=0

For having infinite solutions,

the condition it should satisfy is 

\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\: \: \: -(3)

 

After comparing the equation 1 and equation 2 with equation 3

a_1=c,b_1=3,c_1=3-c

a_2=12,b_2=c,c_2=-c

Putting these values in equation (3)

\frac{c}{12}=\frac{3}{c}=\frac{3-c}{-c}

Equating a pair once we get,

\frac{c}{12}=\frac{3}{c}

c^2=36

c=\pm 6

Hence the value of c=\pm 6.

Posted by

Safeer PP

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