Question

\(\frac{x}{-2}=\frac{y}{7}=\frac{z}{3}và2x+3y-4z=25\)

Answer 1

ta có: \(\frac{x}{-2}=\frac{y}{7}=\frac{z}{3}=\frac{2x}{-4}=\frac{3y}{21}=\frac{4z}{12}\)

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có: \(\frac{2x}{-4}=\frac{3y}{21}=\frac{4z}{12}=\frac{2x+3y-4z}{-4+21-12}=\frac{25}{5}=5\)

\(\Rightarrow\frac{x}{-2}=5\Rightarrow x=-10\)

\(\frac{y}{7}=5\Rightarrow y=35\)

\(\frac{z}{3}=5\Rightarrow z=15\)

KL: x  = -10; y = 35; z = 15

Answer 2

\(\frac{x}{-2}=\frac{y}{7}=\frac{z}{3}\)

\(\Leftrightarrow\)\(\frac{2x}{-4}=\frac{3y}{21}=\frac{4z}{12}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có : 

\(\frac{2x}{-4}=\frac{3y}{21}=\frac{4z}{12}=\frac{2x+3y-4z}{-4+21-12}=\frac{25}{5}=5\)

Do đó : 

\(\frac{x}{-2}=5\)\(\Rightarrow\)\(x=5.\left(-2\right)=-10\)

\(\frac{y}{7}=5\)\(\Rightarrow\)\(y=5.7=35\)

\(\frac{z}{3}=5\)\(\Rightarrow\)\(z=5.3=15\)

Vậy \(x=-10\)\(;\)\(y=35\) và \(z=15\)

Chúc bạn học tốt ~ 

Answer 3

\(\frac{x}{-2}=\frac{y}{7}=\frac{z}{3}=\frac{2x}{-4}=\frac{3y}{21}=\frac{4z}{12}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\frac{2x}{-4}=\frac{3y}{21}=\frac{4z}{12}=\frac{2x+3y-4z}{-4+21-12}=\frac{25}{5}=5\)

\(\Rightarrow\frac{2x}{-4}=5\Rightarrow x=-10\)

\(\frac{3y}{21}=5\Rightarrow y=35\)

\(\frac{4z}{12}=5\Rightarrow z=15\)

KL:.....................................

Answer 4

Có \(\frac{x}{-2}=\frac{y}{7}=\frac{z}{3}\left(2x+3y-4z=25\right)\)

\(\Rightarrow\frac{2x}{-4}=\frac{3y}{21}=\frac{4z}{12}\)

Áp dụng tính chất của dãy tỉ số bằng nhau:

\(\frac{2x}{-4}=\frac{3y}{21}=\frac{4z}{12}=\frac{2x+3y-4z}{-4+21-12}=\frac{25}{5}=5\)

\(\Rightarrow\frac{2x}{-4}=5\Rightarrow2x=\left(-20\right)\Rightarrow x=-10\)

\(\frac{3y}{21}=5\Rightarrow3y=105\Rightarrow y=35\)

\(\frac{4z}{12}=5\Rightarrow4z=60\Rightarrow z=15\)

Vậy x = -10 ; y = 35 ; z = 15