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Question Number 5966 by Kasih last updated on 07/Jun/16

equation (1) 2A+5B+C+29=0 equation (2) 9A+6B+C+117=0 equation (3) 3A−2B+C+13=0 A=...? B=...? C=...?

$${equation}\:\left(\mathrm{1}\right)\:\mathrm{2}{A}+\mathrm{5}{B}+{C}+\mathrm{29}=\mathrm{0} \\ $$$${equation}\:\left(\mathrm{2}\right)\:\mathrm{9}{A}+\mathrm{6}{B}+{C}+\mathrm{117}=\mathrm{0} \\ $$$${equation}\:\left(\mathrm{3}\right)\:\mathrm{3}{A}−\mathrm{2}{B}+{C}+\mathrm{13}=\mathrm{0} \\ $$$${A}=...?\:{B}=...?\:{C}=...? \\ $$

Answered by Ashis last updated on 07/Jun/16

A=−12 B=−4 C=15

$${A}=−\mathrm{12} \\ $$$${B}=−\mathrm{4} \\ $$$${C}=\mathrm{15} \\ $$

Answered by Rasheed Soomro last updated on 09/Jun/16

{ ((9A+6B+C+117=0 )),(( Minus_(∣) ^(∣) →)),((2A+5B+C+29=0)) :} { (),() :}7A+B+88=0⇒56A+8B+704=0 (i) MINUS_(∣) ^(∣) { ((9A+6B+C+117=0)),(( Minus_( ∣) ^(∣) →)),((3A−2B+C+13=0)) :} { (),() :}6A+8B+104=0⇒6A+8B+104=0_(↓) (ii) ⇒ 50A+600=0⇒A=−12 7A+B+88=0⇒7(−12)+B=−88⇒B=−88+84=−4 2A+5B+C+29=0⇒2(−12)+5(−4)+C=−29 ⇒C=−29+44=15

$$\begin{cases}{\mathrm{9}{A}+\mathrm{6}{B}+{C}+\mathrm{117}=\mathrm{0}\:}\\{\:\:\:\:\:\:\:\:\underset{\mid} {\:{Minus}}\rightarrow}\\{\mathrm{2}{A}+\mathrm{5}{B}+{C}+\mathrm{29}=\mathrm{0}}\end{cases}\begin{cases}{}\\{}\end{cases}\mathrm{7}{A}+{B}+\mathrm{88}=\mathrm{0}\Rightarrow\mathrm{56}{A}+\mathrm{8}{B}+\mathrm{704}=\mathrm{0}\:\left({i}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{\mid} {\overset{\mid} {\mathrm{MINUS}}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\begin{cases}{\mathrm{9}{A}+\mathrm{6}{B}+{C}+\mathrm{117}=\mathrm{0}}\\{\:\:\:\:\:\:\:\:\:\:\:\underset{\:\mid} {\:{Minus}}\rightarrow}\\{\mathrm{3}{A}−\mathrm{2}{B}+{C}+\mathrm{13}=\mathrm{0}}\end{cases}\begin{cases}{}\\{}\end{cases}\mathrm{6}{A}+\mathrm{8}{B}+\mathrm{104}=\mathrm{0}\Rightarrow\underset{\downarrow} {\mathrm{6}{A}+\mathrm{8}{B}+\mathrm{104}=\mathrm{0}}\:\left({ii}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\mathrm{50}{A}+\mathrm{600}=\mathrm{0}\Rightarrow{A}=−\mathrm{12} \\ $$$$ \\ $$$$\mathrm{7}{A}+{B}+\mathrm{88}=\mathrm{0}\Rightarrow\mathrm{7}\left(−\mathrm{12}\right)+{B}=−\mathrm{88}\Rightarrow{B}=−\mathrm{88}+\mathrm{84}=−\mathrm{4} \\ $$$$ \\ $$$$\mathrm{2}{A}+\mathrm{5}{B}+{C}+\mathrm{29}=\mathrm{0}\Rightarrow\mathrm{2}\left(−\mathrm{12}\right)+\mathrm{5}\left(−\mathrm{4}\right)+{C}=−\mathrm{29} \\ $$$$\Rightarrow{C}=−\mathrm{29}+\mathrm{44}=\mathrm{15} \\ $$

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