[tex]\left \{ {{4x-3y=5k-6} \atop {-4x+y=k+2}} \right. \\
\left \{ {{4x=3y+5k-6} \atop {-(3y+5k-6)+y=k+2}} \right. \\
\left \{ {{4x=3y+5k-6} \atop {-3y-5k+6+y=k+2}} \right. \\
\left \{ {{4x=3y+5k-6} \atop {-2y=6k-4}} \right. \\
\left \{ {{4x=3y+5k-6} \atop {y=-3k+2}} \right. \\
\left \{ {{4x=-9k+6+5k-6} \atop {y=-3k+2}} \right. \\
\left \{ {{4x=-4k} \atop {y=-3k+2}} \right.\\
\left \{ {{x=-k} \atop {y=-3k+2}} \right.[/tex]
a)
[tex]\left \{ {{x>0} \atop {y>0}} \right. \\
\left \{ {{-k>0} \atop {-3k+2>0}} \right. \\
\left \{ {{k<0} \atop {-3k>-2}} \right. \\
\left \{ {{k<0} \atop {k<\frac{2}{3}}} \right.[/tex]
Z obu warunków [tex]k<0[/tex] czyli [tex]k\in(-\infty,0)[/tex].
b)
[tex]\left \{ {{x<0} \atop {y<0}} \right. \\\left \{ {{-k<0} \atop {-3k+2<0}} \right. \\\left \{ {{k>0} \atop {-3k<-2}} \right. \\\left \{ {{k>0} \atop {k>\frac{2}{3}}} \right.[/tex]
Z obu warunków [tex]k>\frac{2}{3}[/tex] czyli [tex]k\in(\frac{2}{3},+\infty)[/tex].
c)
Tu jest suma przedziałów z podpunktów a i b, czyli [tex]k\in(-\infty,0)\cup(\frac{2}{3},+\infty)[/tex].
