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Question Number 123184 by solstis last updated on 23/Nov/20

{ ((x + y= 8)),((2x − 3y=−5 )) :} the number 8 is wrong? i solved it many times x= 5 y=5 another answers x= (7/5) y= ((13)/5) please help

$$\begin{cases}{{x}\:+\:{y}=\:\mathrm{8}}\\{\mathrm{2}{x}\:−\:\mathrm{3}{y}=−\mathrm{5}\:}\end{cases} \\ $$$$ \\ $$$$\mathrm{the}\:\mathrm{number}\:\mathrm{8}\:\mathrm{is}\:\mathrm{wrong}?\: \\ $$$$\mathrm{i}\:\mathrm{solved}\:\mathrm{it}\:\mathrm{many}\:\mathrm{times}\:\:\mathrm{x}=\:\mathrm{5}\:\:\mathrm{y}=\mathrm{5} \\ $$$$\mathrm{another}\:\mathrm{answers}\:\:\mathrm{x}=\:\frac{\mathrm{7}}{\mathrm{5}}\:\:\:\mathrm{y}=\:\frac{\mathrm{13}}{\mathrm{5}}\: \\ $$$$\mathrm{please}\:\mathrm{help} \\ $$

Commented by MJS_new last updated on 23/Nov/20

how did you solve it??? I get x=((19)/5) and y=((21)/5)

$$\mathrm{how}\:\mathrm{did}\:\mathrm{you}\:\mathrm{solve}\:\mathrm{it}??? \\ $$$$\mathrm{I}\:\mathrm{get}\:{x}=\frac{\mathrm{19}}{\mathrm{5}}\:\mathrm{and}\:{y}=\frac{\mathrm{21}}{\mathrm{5}} \\ $$

Commented by MJS_new last updated on 23/Nov/20

how could it be x=y=5 when x+y=8? how could it be x=(7/5) and y=((13)/5) when x+y=8?

$$\mathrm{how}\:\mathrm{could}\:\mathrm{it}\:\mathrm{be}\:{x}={y}=\mathrm{5}\:\mathrm{when}\:{x}+{y}=\mathrm{8}? \\ $$$$\mathrm{how}\:\mathrm{could}\:\mathrm{it}\:\mathrm{be}\:{x}=\frac{\mathrm{7}}{\mathrm{5}}\:\mathrm{and}\:{y}=\frac{\mathrm{13}}{\mathrm{5}}\:\mathrm{when}\:{x}+{y}=\mathrm{8}? \\ $$

Commented by JDamian last updated on 23/Nov/20

Are you kidding? Your solutions are wrong but you question de data?!!

Commented by Lordose last updated on 23/Nov/20

That was what I wanted to ask It's kinda funny though

Commented by solstis last updated on 23/Nov/20

thank for answer bro i got the solution like this. im so stupid sorry for that question guys x+y= 8 x=8−y 2×(8−y)−3y=−5 16−2y−3y=−5 5y=−5−16 y= ((−21)/(−5)) x= 8−((21)/5) x= ((19)/5)

$$ \\ $$$$\mathrm{thank}\:\mathrm{for}\:\mathrm{answer}\:\mathrm{bro}\:\:\mathrm{i}\:\mathrm{got}\:\mathrm{the}\:\mathrm{solution}\: \\ $$$$\mathrm{like}\:\mathrm{this}.\:\mathrm{im}\:\mathrm{so}\:\mathrm{stupid}\:\mathrm{sorry}\:\mathrm{for}\:\mathrm{that}\:\mathrm{question}\:\mathrm{guys} \\ $$$$\mathrm{x}+\mathrm{y}=\:\mathrm{8} \\ $$$$\mathrm{x}=\mathrm{8}−\mathrm{y} \\ $$$$ \\ $$$$\mathrm{2}×\left(\mathrm{8}−\mathrm{y}\right)−\mathrm{3y}=−\mathrm{5} \\ $$$$\mathrm{16}−\mathrm{2y}−\mathrm{3y}=−\mathrm{5} \\ $$$$\mathrm{5y}=−\mathrm{5}−\mathrm{16} \\ $$$$\mathrm{y}=\:\frac{−\mathrm{21}}{−\mathrm{5}} \\ $$$$ \\ $$$$\mathrm{x}=\:\mathrm{8}−\frac{\mathrm{21}}{\mathrm{5}} \\ $$$$\mathrm{x}=\:\frac{\mathrm{19}}{\mathrm{5}} \\ $$

Answered by Lordose last updated on 23/Nov/20

x + y = 8 −−−(1) 2x − 3y = −5 −−−(2) (1)×2: 2x + 2y = 16 −−−(3) (2)×1: 2x − 3y = −5 −−−(4) (3) − (4): 5y = 21 ⇒ y=((21)/5) Sub in (1) x + ((21)/5) = 8 x = 8−((21)/5) x = ((40−21)/5) x = ((19)/5) (x,y) = (((19)/5),((21)/5))

$$ \\ $$$$\mathrm{x}\:+\:\mathrm{y}\:=\:\mathrm{8}\:\:\:−−−\left(\mathrm{1}\right) \\ $$$$\mathrm{2x}\:−\:\mathrm{3y}\:=\:−\mathrm{5}\:\:\:−−−\left(\mathrm{2}\right) \\ $$$$\left(\mathrm{1}\right)×\mathrm{2}:\:\mathrm{2x}\:+\:\mathrm{2y}\:=\:\mathrm{16}\:−−−\left(\mathrm{3}\right) \\ $$$$\left(\mathrm{2}\right)×\mathrm{1}:\:\mathrm{2x}\:−\:\mathrm{3y}\:=\:−\mathrm{5}\:−−−\left(\mathrm{4}\right) \\ $$$$\left(\mathrm{3}\right)\:−\:\left(\mathrm{4}\right):\:\mathrm{5y}\:=\:\mathrm{21}\:\Rightarrow\:\mathrm{y}=\frac{\mathrm{21}}{\mathrm{5}} \\ $$$$\mathrm{Sub}\:\mathrm{in}\:\left(\mathrm{1}\right) \\ $$$$\mathrm{x}\:+\:\frac{\mathrm{21}}{\mathrm{5}}\:=\:\mathrm{8} \\ $$$$\mathrm{x}\:=\:\mathrm{8}−\frac{\mathrm{21}}{\mathrm{5}} \\ $$$$\mathrm{x}\:=\:\frac{\mathrm{40}−\mathrm{21}}{\mathrm{5}} \\ $$$$\mathrm{x}\:=\:\frac{\mathrm{19}}{\mathrm{5}} \\ $$$$\left(\mathrm{x},\mathrm{y}\right)\:=\:\left(\frac{\mathrm{19}}{\mathrm{5}},\frac{\mathrm{21}}{\mathrm{5}}\right) \\ $$

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