Zadanie 1.
[tex]\left \{ {{6x+2y=2} \atop {-8x-y=9}} \right. \\\left \{ {{2y=2-6x\ |:2} \atop {-8x-y=9}} \right. \\\left \{ {{y=1-3x} \atop {-8x-(1-3x)=9}} \right. \\\left \{ {{y=1-3x} \atop {-8x-1+3x=9}} \right.\\\left \{ {{y=1-3x} \atop {-5x=10\ |:(-5)}} \right.\\\left \{ {{x=-2} \atop {y=1-3*(-2)}} \right.\\\left \{ {{x=-2} \atop {y=7}} \right.[/tex]
Sprawdzenie
[tex]\left \{ {{6*(-2)+2*7=2} \atop {-8*(-2)-7=9}} \right. \\\left \{ {{-12+14=2} \atop {16-7=9}} \right. \\\left \{ {{2=2} \atop {9=9}} \right.[/tex]
Zadanie 2.
[tex]\left \{ {{16x+2y=-2} \atop {12x+y=0}} \right. \\\left \{ {{16x+2y=-2} \atop {y=-12x}} \right. \\\left \{ {{16x+2*(-12x)=-2} \atop {y=-12x}} \right. \\\left \{ {{16x-24x=-2} \atop {y=-12x}} \right. \\\left \{ {{-8x=-2\ |:(-8)} \atop {y=-12x}} \right. \\\left \{ {{x=\frac{1}{4}} \atop {y=-12*\frac{1}{4}}}} \right. \\\left \{ {{x=\frac{1}{4}} \atop {y=-3}}} \right.[/tex]
Sprawdzenie
[tex]\left \{ {{16*\frac{1}{4}+2*(-3)=-2} \atop {12*\frac{1}{4}-3=0}} \right. \\\left \{ {{4-6=-2} \atop {3-3=0}} \right. \\\left \{ {{-2=-2} \atop {0=0}} \right.[/tex]
Zadanie 3.
[tex]\left \{ {{2x+3y=5} \atop {3x-y=13\ |*3}} \right. \\\left \{ {{2x+3y=5} \atop {9x-3y=39}} \right|+\\\left \{ {{11x=44\ |:11\atop {2x+3y=5}} \right.\\\left \{ {{x=4 \atop {2*4+3y=5}} \right.\\\left \{ {{x=4 \atop {8+3y=5}} \right.\\\\\left \{ {{x=4 \atop {3y=-3\ |:3}} \right.\\\left \{ {{x=4 \atop {y=-1}} \right.[/tex]
Zadanie 4.
[tex]\left \{ {{5x+7y=3\ |*4} \atop {3x-4y=10\ |*7}} \right. \\\left \{ {{20x+28y=12} \atop {21x-28y=70}} \right|+\\ \left \{ {{41x=82\ |:41} \atop {5x+7y=3}} \right.\\ \left \{ {{x=2} \atop {5*2+7y=3}} \right.\\ \left \{ {{x=2} \atop {10+7y=3}} \right.\\ \left \{ {{x=2} \atop {7y=-7\ |:7}} \right.\\ \left \{ {{x=2} \atop {y=-1}} \right.[/tex]
Zadanie 5.
x - cena 1 hot-doga
y - cena 1 puszki napoju
[tex]\left \{ {{5x+3y=34\ |*(-1)} \atop {5x+4y=37}} \right. \\\left \{ {{-5x-3y=-34} \atop {5x+4y=37}} \right|+\\\left \{ {{y=3} \atop {5x+4*3=37}} \right. \\\left \{ {{y=3} \atop {5x+12=37}} \right. \\\left \{ {{y=3} \atop {5x=25\ |:5}} \right. \\\left \{ {{y=3} \atop {x=5}} \right. \\\left \{ {{x=5} \atop {y=3}} \right.[/tex]
Odp. Jeden hot-dog kosztuje 5 zł, a jedna puszka napoju 3 zł.
