Question

Answer 1

a: \(\frac{x}{3}=\frac{2}{y}\)

=>\(xy=2\cdot3=6\)

=>(x;y)∈{(1;6);(6;1);(-1;-6);(-6;-1);(2;3);(3;2);(-2;-3);(-3;-2)}

b: \(\frac{-3}{x}=\frac{y}{2}\)

=>\(xy=-3\cdot2=-6\)

=>(x;y)∈{(1;-6);(-6;1);(-1;6);(6;-1);(2;-3);(-3;2);(-2;3);(3;-2)}

c: \(\frac{x}{y}=\frac34\)

=>\(\frac{x}{y}=\frac{3k}{4k}\)

=>x=3k; y=4k(k∈Z; k<>0)

d: \(\frac{x}{6}=\frac{y}{8}\)

=>\(\frac{x}{3}=\frac{y}{4}=k\)

=>x=3k; y=4k(k∈Z)