Question

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Answer 1

a) \(\dfrac{x}{y}=\dfrac{5}{7}\)

\(\Rightarrow\dfrac{x}{5}=\dfrac{y}{7}=\dfrac{2x}{10}=\dfrac{2x+y}{10+7}=\dfrac{17}{17}=1\)

\(\Rightarrow\left\{{}\begin{matrix}x=1.5=5\\y=1.7=7\end{matrix}\right.\)

b) \(\Rightarrow\dfrac{x}{1,2}=\dfrac{y}{2,5}=\dfrac{y-x}{2,5-1,2}=\dfrac{26}{1,3}=20\)

\(\Rightarrow\left\{{}\begin{matrix}x=20.1,2=24\\y=20.2,5=50\end{matrix}\right.\)

c) \(\Rightarrow\dfrac{x}{7}=\dfrac{y}{3}=\dfrac{5x}{35}=\dfrac{2y}{6}=\dfrac{5x-2y}{35-6}=\dfrac{87}{29}=3\)

\(\Rightarrow\left\{{}\begin{matrix}x=3.7=21\\y=3.3=9\end{matrix}\right.\)

d) \(\Rightarrow\dfrac{x}{11}=\dfrac{y}{3}=\dfrac{y-x}{3-11}=\dfrac{-16}{-8}=2\)

\(\Rightarrow\left\{{}\begin{matrix}x=2.11=22\\y=2.3=6\end{matrix}\right.\)

e) \(\Rightarrow\dfrac{x}{4}=\dfrac{y}{-5}=\dfrac{2x}{8}=\dfrac{3y}{-15}=\dfrac{2x+3y}{8-15}=\dfrac{21}{-7}=-3\)

\(\Rightarrow\left\{{}\begin{matrix}x=\left(-3\right).4=-12\\y=\left(-3\right).\left(-5\right)=15\end{matrix}\right.\)