Find-the-values-of-k-for-which-the-equation-k-3-10-k-1-x-y-k-1-8-have-a-a-unique-solution-b-no-solution-c-an-infinite-solution-hence-Find-the-image-o

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Question Number 35460 by Rio Mike last updated on 19/May/18

Find the values of k for which the equation (((k −3)),((10 −k+1)) ) ((x),(y) ) = (((k−1)),(8) ) have a) a unique solution b) no solution c)an infinite solution hence Find the image of the point (3,1) after reflection in the line with equation a) x=1 b) y= −1 c) y+x= 1

$${Find}\:{the}\:{values}\:{of}\:{k}\:{for}\:{which} \\ $$$${the}\:{equation}\: \\ $$$$\begin{pmatrix}{{k}\:\:\:\:\:\:\:\:\:−\mathrm{3}}\\{\mathrm{10}\:\:\:\:\:\:\:−{k}+\mathrm{1}}\end{pmatrix}\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\:=\:\begin{pmatrix}{{k}−\mathrm{1}}\\{\mathrm{8}}\end{pmatrix} \\ $$$${have} \\ $$$$\left.{a}\right)\:{a}\:\:{unique}\:{solution} \\ $$$$\left.{b}\right)\:{no}\:{solution} \\ $$$$\left.{c}\right){an}\:{infinite}\:{solution} \\ $$$${hence} \\ $$$${Find}\:{the}\:{image}\:{of}\:{the}\:{point}\: \\ $$$$\left(\mathrm{3},\mathrm{1}\right)\:{after}\:{reflection}\:{in}\:{the}\:{line} \\ $$$${with}\:{equation} \\ $$$$\left.{a}\left.\right)\left.\:{x}=\mathrm{1}\:\:\:\:{b}\right)\:{y}=\:−\mathrm{1}\:\:\boldsymbol{{c}}\right)\:\boldsymbol{{y}}+\boldsymbol{{x}}=\:\mathrm{1} \\ $$

Commented by tanmay.chaudhury50@gmail.com last updated on 19/May/18