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Question Number 54659 by Gulay last updated on 08/Feb/19

Commented by Gulay last updated on 08/Feb/19

$sir could you help me ?$
Commented by maxmathsup by imad last updated on 08/Feb/19
$(s) ⇔ { ((−2x+y =7)),((−kx +y =9)) :} Δ_s = determinant (((−2 1)),((−k 1)))=k−2 so if k≠2 the sy stem have one solution (x,y) with x =(Δ_x /Δ) =( determinant (((7 1)),((9 1)))/(k−2)) =((−2)/(k−2)) and y =( determinant (((−2 7)),((−k 9)))/(k−2)) =((7k−18)/(k−2)) if k =2 we get (s) { ((−2x+y =7)),((−2x +y =9 and the system haven t any solution .)) :}$
$(s) \Leftrightarrow {\begin{cases} - 2 x + y = 7 \\ - k x + y = 9 \end{cases}$ $Δ_{s} = \| \begin{matrix} - 2 1 \\ - k 1 \end{matrix} \| = k - 2 s o i f k \neq 2 t h e s y s t e m h a v e o n e s o l u t i o n$ $(x, y) w i t h x = \frac{Δ_{x}}{Δ} = \frac{\| \begin{matrix} 7 1 \\ 9 1 \end{matrix} \|}{k - 2} = \frac{- 2}{k - 2} a n d y = \frac{\| \begin{matrix} - 2 7 \\ - k 9 \end{matrix} \|}{k - 2} = \frac{7 k - 18}{k - 2}$ $i f k = 2 w e g e t (s) {\begin{cases} - 2 x + y = 7 \\ - 2 x + y = 9 a n d t h e s y s t e m h a v e n t a n y s o l u t i o n . \end{cases}$
	Answered by peter frank last updated on 08/Feb/19

	$y - y - 2 x - (- k x) = 7 - 9 = - 2$ $x (k - 2) = - 2$ $x = \frac{- 2}{k - 2}$ $y = \frac{6 k - 14}{k - 2}$
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