Question

Tìm x và y biết rằng:

a) x/2 = y/3 và x + y = -15

b) 3x = 7y và x - y = -16

c) x/3 = y/4 và xy = 12

Answer 1

a) \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{x+y}{2+3}=\dfrac{-15}{5}=-3\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=\left(-3\right).2=-6\\y=\left(-3\right).3=-9\end{matrix}\right.\)

b) \(3x=7y\Rightarrow\dfrac{x}{7}=\dfrac{y}{3}=\dfrac{x-y}{7-3}=\dfrac{-16}{4}=-4\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=\left(-4\right).7=-28\\y=\left(-4\right).3=-12\end{matrix}\right.\)

c) Đặt \(\dfrac{x}{3}=\dfrac{y}{4}=k\Rightarrow x=3k;y=4k\)

\(\Leftrightarrow xy=3k.4k=12k^2=12\)

\(\Rightarrow k=\left\{-1;1\right\}\)

\(\Rightarrow\left\{{}\begin{matrix}x_1=3;y_1=4\\x_2=-3;y_2=-4\end{matrix}\right.\)

Answer 2

a, \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{x+y}{2+3}=\dfrac{-15}{5}=-3\)

<=> \(\left\{{}\begin{matrix}x=\left(-3\right).2=-6\\y=\left(-3\right).3=-9\end{matrix}\right.\)
@Phạm Hải Minh

Answer 3

b, 3x = 7y => \(\dfrac{x}{7}=\dfrac{y}{3}=\dfrac{x-y}{7-3}=\dfrac{-16}{4}=-4\)

<=> \(\left\{{}\begin{matrix}x=\left(-4\right).7=-28\\y=\left(-4\right).3=-12\end{matrix}\right.\)
@Phạm Hải Minh

Answer 4

c, Đặt \(\dfrac{x}{3}=\dfrac{y}{4}=k\Rightarrow x=3k;y=4k\)

<=> xy = 3k.4k = 12k² = 12
=> k = {-1; 1}
=> \(\left\{{}\begin{matrix}x_1=3;y_1=4\\x_2=-3;y_2=-4\end{matrix}\right.\)
@Phạm Hải Minh