Question

For what value of k will pair of equations have no solution? 3x+y=1 , (2k-1)x+(k-1)y=2k+1

Answer 1

${ \large{ \sf{ \underbrace{\underline{\bigstar \: Answer}}}}}$

$\sf\color{darkviolet}{3x \:+y =\: 1 ; (2k –1) \:x + (k \:–1) y =\: 2k + \:1}$

$\sf\color{green}{ 3x \:+y \:= 1}$

$\textbf{Subtract 1 both side we get}$

$\sf\color{skyblue}{3x\: +\: y –\: 1 = 0}$

$\sf\color{red}{(2k –1) \:x + \:(k –1)\: y \: = 2k\: + 1}$

$\textbf{Subtract 2k +1 both side we get}$

$\sf\color{pink}{(2k –1)\: x + \:(k –1) y – \:(2k + 1)= \:0}$

$\textbf{3x\:+\:y=\:1}$

$\tt{And}$

$\sf\color{purple}{(2k-1)\:x+\:(k-1)\:y=\:2k\:+1}$

$\textbf{They can be rewrite as:}$

$\sf\color{aqua}{3x \:+ y\: – \:1 =\: 0}$

$\tt{and}$

$\sf\color{orange}{(2k-1)\:x + \:(k-1)y\: (2k+1) =\: 0}$

$\textbf{Cross multiply we get}$

$\sf\color{maroon}{ 3k –\: 3 \:= 2k\: –\: 1}$

$\sf\color{gold}{ = 3\:-1}$

$\sf\color{indigo}{k \:= \:2}$

${ \large{ \boxed{ \red{ \underline{ \bf \:Hence \:Answer \:is\: k\: =\: 2}}}}}$

Thankyou :)

You can also refer the attachment :)

Answer 2

$\huge\bf{Question:-}$

For what value of k will pair of equations have no solution? 3x+y=1 , (2k-1)x+(k-1)y=2k+1

$\huge\bf{Solution:-}$

(Refer to attachment)

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