Cześć!
[tex]\left \{ {{x+3y=a+1} \atop {2x-y=a}} \right.[/tex]
Budujemy wyznaczniki:
[tex]W = \left[\begin{array}{ccc}1&3\\2&-1\end{array}\right] = -1-6=-7\\\\W_x = \left[\begin{array}{ccc}a+1&3\\a&-1\end{array}\right] = -a-1-3a=-4a-1\\\\W_y = \left[\begin{array}{ccc}1&a+1\\2&a\end{array}\right] = a-2a-2=-a-2[/tex]
[tex]x =\frac{W_x}{W} = \frac{-4a-1}{-7} =\frac{4a+1}{7}\\\\y= \frac{W_y}{W} = \frac{-a-2}{-7} = \frac{a+2}{7}[/tex]
[tex]x+2y > 1 \iff \frac{4a+1}{7} + \frac{2a+4}{7} > 1 \iff \frac{6a+5}{7} -\frac{7}{7} > 0 \iff\\\\\iff \frac{6a-2}{7} > 0 \iff 6a-2 > 0 \iff a > \frac{1}{3}[/tex]
Pozdrawiam!
