Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 10675 by niraj last updated on 22/Feb/17

given that x,y∈R solve.  (1) (x+2y)+i(2x−3y)=5−4i  (2) (x+iy)×(7−5i)=9+4i

$${given}\:{that}\:{x},{y}\in{R}\:{solve}. \\ $$$$\left(\mathrm{1}\right)\:\left({x}+\mathrm{2}{y}\right)+{i}\left(\mathrm{2}{x}−\mathrm{3}{y}\right)=\mathrm{5}−\mathrm{4}{i} \\ $$$$\left(\mathrm{2}\right)\:\left({x}+{iy}\right)×\left(\mathrm{7}−\mathrm{5}{i}\right)=\mathrm{9}+\mathrm{4}{i} \\ $$

Commented by niraj last updated on 22/Feb/17

sir answer please

$${sir}\:{answer}\:{please} \\ $$

Answered by sandy_suhendra last updated on 22/Feb/17

1) x+2y=5 ⇒ x=5−2y     2x−3y=−4     2(5−2y)−3y=−4    10−4y−3y=−4       −7y=−14 ⇒y=2  x=5−2(2)=1    2)7x−5ix+7iy+5y=9+4i      (7x+5y)+i(−5x+7y)=9+4i      7x+5y=9...(×5)⇒    35x+25y=45  −5x+7y=4...(×7)⇒−35x+49y=28                                                   −−−−−−−−−(+                                                       74y=73                                                      y=((73)/(74))  7x+5(((73)/(74)))=9  7x=((301)/(74))  x=((43)/(74))

$$\left.\mathrm{1}\right)\:\mathrm{x}+\mathrm{2y}=\mathrm{5}\:\Rightarrow\:\mathrm{x}=\mathrm{5}−\mathrm{2y} \\ $$$$\:\:\:\mathrm{2x}−\mathrm{3y}=−\mathrm{4} \\ $$$$\:\:\:\mathrm{2}\left(\mathrm{5}−\mathrm{2y}\right)−\mathrm{3y}=−\mathrm{4} \\ $$$$\:\:\mathrm{10}−\mathrm{4y}−\mathrm{3y}=−\mathrm{4} \\ $$$$\:\:\:\:\:−\mathrm{7y}=−\mathrm{14}\:\Rightarrow\mathrm{y}=\mathrm{2} \\ $$$$\mathrm{x}=\mathrm{5}−\mathrm{2}\left(\mathrm{2}\right)=\mathrm{1} \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\mathrm{7x}−\mathrm{5ix}+\mathrm{7iy}+\mathrm{5y}=\mathrm{9}+\mathrm{4i} \\ $$$$\:\:\:\:\left(\mathrm{7x}+\mathrm{5y}\right)+\mathrm{i}\left(−\mathrm{5x}+\mathrm{7y}\right)=\mathrm{9}+\mathrm{4i} \\ $$$$\:\:\:\:\mathrm{7x}+\mathrm{5y}=\mathrm{9}...\left(×\mathrm{5}\right)\Rightarrow\:\:\:\:\mathrm{35x}+\mathrm{25y}=\mathrm{45} \\ $$$$−\mathrm{5x}+\mathrm{7y}=\mathrm{4}...\left(×\mathrm{7}\right)\Rightarrow−\mathrm{35x}+\mathrm{49y}=\mathrm{28}\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−−−−−−−−−\left(+\:\:\:\:\:\right. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{74y}=\mathrm{73} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}=\frac{\mathrm{73}}{\mathrm{74}} \\ $$$$\mathrm{7x}+\mathrm{5}\left(\frac{\mathrm{73}}{\mathrm{74}}\right)=\mathrm{9} \\ $$$$\mathrm{7x}=\frac{\mathrm{301}}{\mathrm{74}} \\ $$$$\mathrm{x}=\frac{\mathrm{43}}{\mathrm{74}} \\ $$

Commented by niraj last updated on 23/Feb/17

very very thanks sir

$${very}\:{very}\:{thanks}\:{sir} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com