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  • For what value of , does the system of linear equations

For what value of k, does the system of linear equations
2x+3y=7
(k-1)x+(k+2)y=3k
have an infinite number of solutions ?

 

 

 

 
 
 
 
 

Answers (1)

For infinite solutions, the linear should be coincident

\Rightarrow \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}

Equation 1\Rightarrow 2x+3y=7

Equation 2\Rightarrow (k-1)k+(k+2)y=3k

\Rightarrow \frac{2}{(k-1)}=\frac{3}{(k+2)}=\frac{7}{3k} ______(1)

solving these two \Rightarrow 2(k+2)=3(k-1)

                              \Rightarrow 2k+4=3k-3

                              \Rightarrow k=7

Putting value of k to check the condition _____(1)

\Rightarrow\frac{2}{(7-1)}=\frac{3}{7+2}=\frac{7}{3\times 7}

\Rightarrow\frac{2}{6}=\frac{3}{9}=\frac{1}{3}

\Rightarrow\frac{1}{3}=\frac{1}{3}=\frac{1}{3}

\Rightarrow\; k=7

Posted by

Safeer PP

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