Odpowiedź:
a)
[tex]\left \{ {{x+y = 5} \atop {2x + 7 = -2y}} \right.[/tex]
[tex]\left \{ {{x + y = 5 / * (-2)} \atop {2x + 7 = -2y}} \right.[/tex]
[tex]\left \{ {{-2x - 2y = -10} \atop {2x + 7 = -2y / -7 + 2y}} \right.[/tex]
[tex]\left \{ {{-2x -2y = -10} \atop {2x + 2y = -7}} \right.[/tex]
-2x + 2x - 2y + 2y = -17
0 = -17
[tex]0\neq -17[/tex] czyli brak rozwiązania
b)
[tex]\left \{ {{x + 2y = 4} \atop {-2x + 8= 4y} \right.[/tex]
[tex]\left \{ {{x + 2y = 4 / * 2} \atop {-2x + 8 = 4y}} \right.[/tex]
[tex]\left \{ {{2x + 4y = 8} \atop {-2x + 8 = 4y / -8 - 4y}} \right.[/tex]
[tex]\left \{ {{2x + 4y = 8} \atop {-2x - 4y = -8}} \right.[/tex]
2x -2x + 4y -4y = 8-8
0 = 0
[tex]0\neq 0[/tex] czyli nieskończenie wiele rozwiązań
c)
[tex]\left \{ {{x + 1 = y} \atop {2x-4 = y}} \right.[/tex]
[tex]\left \{ {{x + 1 = y / -y -1} \atop {2x-4 = y} / -y + 4} \right.[/tex]
[tex]\left \{ {{x -y = -1} \atop {2x - y = 4}} \right.[/tex]
[tex]\left \{ {{x - y =-1 / * (-2)} \atop {2x-y = 4}} \right.[/tex]
[tex]\left \{ {{-2x + 2y = 2 \atop {2x-y = 4}} \right.[/tex]
-2x + 2x + 1y = 4 + 2
1y = 6 / : 1
y= 6
[tex]\left \{ {{x + 1 = 6}[/tex] za y podstawiamy 6
[tex]\left \{ {{x + 1 = 6 / -1}[/tex]
[tex]\left \{ {{x = 5}[/tex]
[tex]\left \{ {{x =5} \atop {y=6}} \right.[/tex] <---- to wynik czyli 1 rozwiązanie
