Odpowiedź:
A)
metoda przeciwnych współczynników
[tex]\left \{ {{x+y=7} \atop {x-y=2}} \right.[/tex]
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2x=9/:2
x=4,5
4,5+y=7
y=7-4,5
y=2,5
x,y= (4,5 , 2,5)
metoda podstawiania
[tex]\left \{ {{x+y=7} \atop {x-y=2}} \right.[/tex]
[tex]\left \{ {{x=7-y} \atop {7-y-y=2}} \right.[/tex]
[tex]\left \{ {{x=7-y} \atop {-2y=2-7}} \right.[/tex]
[tex]\left \{ {{x=7-y} \atop {-2y=-5/:(-2)}} \right.[/tex]
[tex]\left \{ {{y=2,5} \atop {x=7-2,5}} \right.[/tex]
[tex]\left \{ {{y=2,5} \atop {x=4,5}} \right.[/tex]
B)
metoda przeciwnych współczynników
[tex]\left \{ {{3x+4y=22,5} \atop {2x+y=10/*(-4)}} \right.[/tex]
[tex]\left \{ {{3x+4y=22,5} \atop {-8x-4x=-40}} \right.[/tex]
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-5x=-17,5/:(-5)
x=3,5
3*3,5+4y=22,5
10,5+4y=22,5
4y=22,5-10,5
4y=12/:4
y=3
x,y=(3,5 , 3)
metoda podstawiania
[tex]\left \{ {{3x+4y=22,5} \atop {2x+y=10}} \right.[/tex]
[tex]\left \{ {{3x+4(10-2y)=22,5} \atop {y=10-2x}} \right.[/tex]
[tex]\left \{ {{3x+40-8x=22,5} \atop {y=10-2x}} \right.[/tex]
[tex]\left \{ {{-5x=-17,5/:(-5)} \atop {y=10-2x}} \right.[/tex]
[tex]\left \{ {{x=3,5} \atop {y=10-2*3,5}} \right.[/tex]
[tex]\left \{ {{x=3,5} \atop {y=10-7}} \right.[/tex]
[tex]\left \{ {{x=3,5} \atop {y=3}} \right.[/tex]
Szczegółowe wyjaśnienie:
