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a-x-b-y-c-z-1-3-a-2b-c-2-and-2y-z-1-x-An-altered-form-of-q-187020-In-this-case-solveable-




Question Number 187124 by Rasheed.Sindhi last updated on 13/Feb/23
(a/x)=(b/y)=(c/z)=(1/3) ,  a−2b+c=2  and  −2y+z=1      x=?  An altered form of  q#187020  (In this case solveable)
$$\frac{{a}}{{x}}=\frac{{b}}{{y}}=\frac{{c}}{{z}}=\frac{\mathrm{1}}{\mathrm{3}}\:, \\ $$$${a}−\mathrm{2}{b}+{c}=\mathrm{2}\:\:{and}\:\:−\mathrm{2}{y}+{z}=\mathrm{1}\:\:\:\: \\ $$$${x}=? \\ $$$${An}\:{altered}\:{form}\:{of}\:\:{q}#\mathrm{187020} \\ $$$$\left({In}\:{this}\:{case}\:{solveable}\right) \\ $$
Answered by HeferH last updated on 13/Feb/23
x = 3a   y = 3b  z = 3c   a  + c − 2b = 2   −2(3b) + 3c = 1   3c − 6b = 1   c −2b = (1/3)⇒   a + (1/3) = 2   a = (5/3) ⇒   x = 3((5/3)) = 5
$${x}\:=\:\mathrm{3}{a}\: \\ $$$${y}\:=\:\mathrm{3}{b} \\ $$$${z}\:=\:\mathrm{3}{c} \\ $$$$\:{a}\:\:+\:{c}\:−\:\mathrm{2}{b}\:=\:\mathrm{2} \\ $$$$\:−\mathrm{2}\left(\mathrm{3}{b}\right)\:+\:\mathrm{3}{c}\:=\:\mathrm{1} \\ $$$$\:\mathrm{3}{c}\:−\:\mathrm{6}{b}\:=\:\mathrm{1} \\ $$$$\:{c}\:−\mathrm{2}{b}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\Rightarrow \\ $$$$\:{a}\:+\:\frac{\mathrm{1}}{\mathrm{3}}\:=\:\mathrm{2} \\ $$$$\:{a}\:=\:\frac{\mathrm{5}}{\mathrm{3}}\:\Rightarrow \\ $$$$\:{x}\:=\:\mathrm{3}\left(\frac{\mathrm{5}}{\mathrm{3}}\right)\:=\:\mathrm{5}\: \\ $$
Commented by Rasheed.Sindhi last updated on 14/Feb/23
Thanks sir!
$$\mathbb{T}\boldsymbol{\mathrm{han}}\Bbbk\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{sir}}! \\ $$
Answered by mr W last updated on 13/Feb/23
3(a−2b+c)=3×2  x−2y+z=6  x+1=6  x=5
$$\mathrm{3}\left({a}−\mathrm{2}{b}+{c}\right)=\mathrm{3}×\mathrm{2} \\ $$$${x}−\mathrm{2}{y}+{z}=\mathrm{6} \\ $$$${x}+\mathrm{1}=\mathrm{6} \\ $$$${x}=\mathrm{5} \\ $$
Commented by Rasheed.Sindhi last updated on 14/Feb/23
Smart approach!
$${Smart}\:{approach}! \\ $$
Commented by Rasheed.Sindhi last updated on 14/Feb/23
ThanX sir!
$$\boldsymbol{\mathcal{T}{han}\mathcal{X}}\:\boldsymbol{{sir}}! \\ $$

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