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Question Number 89649 by jagoll last updated on 18/Apr/20
$$\mathrm{If}\:\begin{pmatrix}{\mathrm{a}−\mathrm{b}\:\:\:\:\:\:\mathrm{b}+\mathrm{c}}\\{\mathrm{3d}+\mathrm{c}\:\:\:\:\:\mathrm{2c}−\mathrm{d}}\end{pmatrix}\:=\:\begin{pmatrix}{\mathrm{8}\:\:\:\:\mathrm{1}}\\{\mathrm{7}\:\:\:\:\mathrm{6}}\end{pmatrix} \\ $$$$\mathrm{then}\:\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}\:=\: \\ $$$$\mathrm{A}.\:−\frac{\mathrm{53}}{\mathrm{7}}\:\:\:\:\:\:\:\mathrm{B}.\:−\frac{\mathrm{18}}{\mathrm{7}}\:\:\:\:\:\:\:\mathrm{C}.\:\frac{\mathrm{43}}{\mathrm{7}} \\ $$$$\mathrm{D}.\:\frac{\mathrm{38}}{\mathrm{7}}\:\:\:\:\mathrm{E}.\:\frac{\mathrm{53}}{\mathrm{7}} \\ $$
Commented by jagoll last updated on 18/Apr/20
$$\mathrm{i}'\mathrm{m}\:\mathrm{got}\:\frac{\mathrm{53}}{\mathrm{7}}.\:\mathrm{it}\:\mathrm{correct}\:? \\ $$
Commented by john santu last updated on 18/Apr/20
$$\mathrm{6}{d}\:+\:\mathrm{2}{c}\:=\:\mathrm{24}\: \\ $$$$−{d}\:+\:\mathrm{2}{c}\:=\:\mathrm{6}\: \\ $$$$\:−−−−−−\:− \\ $$$$\mathrm{7}{d}\:=\:\mathrm{18}\:\Rightarrow{d}\:=\:\frac{\mathrm{18}}{\mathrm{7}}\:\wedge\:{c}\:=\:\frac{\mathrm{30}}{\mathrm{7}} \\ $$$$\Rightarrow\:{b}+{c}\:=\:\mathrm{1}\:\Rightarrow\:{b}\:=\:−\frac{\mathrm{23}}{\mathrm{7}} \\ $$$$\Rightarrow{a}−{b}\:=\:\mathrm{8}\:\Rightarrow\:{a}\:=\:\frac{\mathrm{33}}{\mathrm{7}} \\ $$$$\therefore\:{a}+{b}+{c}+{d}\:=\:\frac{\mathrm{58}}{\mathrm{7}} \\ $$$$ \\ $$
Commented by jagoll last updated on 19/Apr/20
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir}.\:\mathrm{you}\:\mathrm{are}\:\mathrm{correct} \\ $$