(5x+2y)/3 = (y-4x)/5 and x+3y=-8 then 13(x+y)=
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S
1
LC
1 tháng 11 2015
Áp dụng tính chất của dãy tỉ số bằng nhau ta có:
\(\frac{5x+2y}{3}=\frac{y-4x}{5}=\frac{5x+2y+y-4x}{3+5}=\frac{x+3y}{8}=\frac{-8}{8}=-1\)
=>5x+2y=-3=>5.(5x+2y)=5.(-3)=>25x+10y=-15
y-4x=-5=>3.(y-4x)=3.(-5)=>3y-12x=-15
=>25x+10y+3y-12x=-15+(-15)
=>13x+13y=-30
=>13.(x+y)=-30
S
0
TT
1
S
19 tháng 3 2020
\(\frac{5x+2y}{3}\text{ equals }\frac{y-4x}{5}\text{ then:}25x+10y=3y-12x\text{ therefore:}37x=-7x\)
\(\Rightarrow\frac{37}{-7}x=y\text{ therefore:}x+3y=\frac{104}{-7}x=-8\Rightarrow x=\frac{13}{7}\Rightarrow y=\frac{13.37}{-49}=...\text{ then}\)
\(\text{COMPUTE IT YOURSELF}\)
LR
0
HX
1
22 tháng 11 2015
\(\frac{5x+2y}{3}=\frac{y-4x}{5}=\frac{5x+2y+y-4x}{3+5}=\frac{x+3y}{8}=-\frac{8}{8}=-1\)
5x+2y =-3
y -4x =-1 => 2y = 8x-2
=> 5x + 8x-2 =-3 => 13x =-1
=> y =4x-1 ==>13y = 4(13x)-13 =4(-1) -1 =-5
=> 13x+13y= 13(x+y)= -1 +(-5) =-6
Vậy 13(x+y) = -6
20 tháng 9 2021
\(a,\left\{{}\begin{matrix}3x-y=5\\4x+2y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x-y=5\\2x+y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\\ b,\left\{{}\begin{matrix}5x+2y=9\\x+5y=11\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5x+2y=9\\5x+25y=55\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5x+2y=9\\23y=46\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=2\end{matrix}\right.\)
\(c,\left\{{}\begin{matrix}3x+y=10\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9x+3y=30\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}13x=39\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=1\end{matrix}\right.\\ d,\left\{{}\begin{matrix}4x+3y=22\\5x+3y=26\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\5x+3y=26\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=2\end{matrix}\right.\)
\(e,\left\{{}\begin{matrix}4x-3y=5\\5x+3y=13\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9x=18\\5x+3y=13\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)
HP
20 tháng 9 2021
a. \(\left\{{}\begin{matrix}3x-y=5\\4x+2y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x-2y=10\\4x+2y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}10x=20\\6x-2y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)
b. \(\left\{{}\begin{matrix}5x+2y=9\\x+5y=11\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5x+2y=9\\5x+25y=55\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}23y=46\\5x+2y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=2\\x=1\end{matrix}\right.\)
c. \(\left\{{}\begin{matrix}3x+y=10\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9x+3y=30\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}13x=39\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=1\end{matrix}\right.\)
d. \(\left\{{}\begin{matrix}4x+3y=22\\5x+3y=26\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\4x+3y=22\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=2\end{matrix}\right.\)
e. \(\left\{{}\begin{matrix}4x-3y=5\\5x+3y=13\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9x=18\\4x-3y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)
Áp dụng tính chất của dãy tỉ số bằng nhau ta có:
\(\frac{5x+2y}{3}=\frac{y-4x}{5}=\frac{5x+2y+y-4x}{3+5}=\frac{x+3y}{8}=\frac{-8}{8}=-1\)
=>5x+2y=-3=>5.(5x+2y)=5.(-3)=>25x+10y=-15
y-4x=-5=>3.(y-4x)=3.(-5)=>3y-12x=-15
=>25x+10y+3y-12x=-15+(-15)
=>13x+13y=-30
=>13.(x+y)=-30