zadaniazmatematyki

zadanie 26 x - cena wiśni za 1kg y - cena czereśni za 1kg 4x = 3y 2y + x = 11 4x - 3y =0 / *2 x + 2y = 11 / * 3 8x - 6y = 0 3x + 6y = 33 8x + 3x = 0 + 33 11x = 33 /: 11 x=3 4x = 3y 4 * 3 = 3y 3y = 12 /:3 y=4 wiśnia kosztuje 3zł/kg, a czereśnia 4zł/kg

zadanie 25 x - ilość psów y - ilość ptaków 4x + 2y = 96 x + y = 40 / * (-2) 4x + 2y = 96 -2x - 2y = -80 4x - 2x = 96 - 80 2x = 16 /:2 x=8 x + y = 40 8 + y = 40 y=40 - 8 y=32 w sklepie jest 8 psów i 32 ptaki

c) x/2 + y/6 = 5/3 /* 6 x/6 + y/2 = 1 /* 6 3x + y = 10 x + 3y = 6 /* (-3) 3x + y = 10 -3x - 9y = -18 y - 9y = 10 - 18 -8y = -8 /: (-8) y=1 x + 3y = 6 x + 3 * 1 = 6 x + 3 = 6 x = 6-3 x=3

b) x/6 + y/2 = 1/2 / *6 x/6 - y/2 = 1/6 /* 6 x + 3y = 3 x - 3y = 1 x + x = 3 + 1 2x = 4 /:2 x=2 x + 3y = 3 2 + 3y = 3 3y = 3-2 3y=1 /:3 y=1/3

zadanie 5 a) x/3 + y/5 = 5 / * 15 x/2 - y/3 = -2 / * 6 5x + 3y = 75 / *2 3x - 2y = -12 /* 3 10x + 6y = 150 9x - 6y = -36 10x + 9x = 150 - 36 19x = 114 /: 19 x=6 3x - 2y = -12 3 * 6 - 2y = -12 18 - 2y = -12 -2y = -12 - 18 -2y = -30 /: (-2) y=15

d) 5/2 x + 1/2 y = -4 /* 2 x - 2y = 5 5x + y = -8 /* 2 x - 2y = 5 10x + 2y = -16 x - 2y = 5 10x + x = -16 + 5 11x = -11 /: 11 x=-1 x - 2y =5 -1 - 2y = 5 -2y = 5 + 1 -2y = 6 /: (-2) y=-3

c) (2x-y)/3 - (3x)/4 = 3/2 /* 12 x+ 4y = 2 4(2x-y) - 3 * 3x = 6 * 3 x + 4y = 2 8x - 4y - 9x = 18 x + 4y = 2 -x - 4y = 18 x + 4y = 2 0=20 układ sprzeczny brak rozwiązania

b) (x-y)/3 - (2x+y)/2 = 10 /* 6 x+2y =0 2(x-y) - 3(2x + y)= 60 x=-2y 2x - 2y - 6x - 3y = 60 x=-2y -4x - 5y = 60 x=-2y -4 * (-2y) - 5y = 60 x=-2y 8y - 5y = 60 x=-2y 3y = 60 /: 3 x=-2y y=20 x=-2y y=20 x=-2 * 20 y=20 x=-40

zadanie 4 x/3 - y/2 = (x+y)/6 /* 6 y=2x-7 2x - 3y = x+y y=2x-7 2x - x = y + 3y y=2x - 7 x = 4y y=2 * 4y - 7 x=4y y=8y - 7 x=4y y-8y = -7 x=4y -7y = -7 /: (-7) x=4y y=1 x=4 * 1 y=1 x=4 y=1

d) 5(3x+y) -8(x-6y)=200 20(2x-3y)-13(x-y)=520 15x + 5y - 8x + 48y = 200 40x - 60y - 13x + 13y = 520 7x + 53y = 200 /* 27 27x - 47y = 520 /* (-7) 189x + 1431y = 5400 -189x + 329 y = - 3640 1431 y + 329 y = 5400 - 3640 1760y = 1760 /: 1760 y=1 27x - 47y = 520 27x - 47 * 1 = 520 27x - 47 = 520 27x = 520 + 47 27x = 567 /: 27 x=21

c) 2(x+y) - 3(x-y) = 4 5(x+y) - 7(x-y) =2 2x + 2y - 3x + 3y = 4 5x + 5y - 7x + 7y = 2 -x + 5y = 4 /* (-2) -2x + 12y = 2 2x - 10y = -8 -2x + 12y = 2 -10y + 12y = -8 + 2 2y = -6 /:2 y=-3 -x + 5y = 4 -x + 5 * (-3) = 4 -x - 15 = 4 -x = 4 + 15 -x = 19 /: (-1) x=-19

zadanie 3 a) 3(x-1)= 4y +1 5(y-1) = x+1 3x - 3 = 4y + 1 5y - 5 = x+ 1 3x - 4y = 1+3 -x + 5y = 1+5 3x - 4y = 4 -x + 5y = 6 /*3 3x - 4y = 4 -3x + 15y = 18 -4y + 15y = 4 + 18 11y = 22 /: 11 y=2 3x - 4y = 4 3x - 4 * 2 = 4 3x - 8 = 4 3x= 4+ 8 3x = 12 /:3 x=4

e) 7x - 3y = 15 /* 2 5x + 6y = 27 14x - 6y = 30 5x + 6y = 27 14x + 5x = 30 + 27 19x = 57 /: 19 x=3 5x + 6y = 27 5 * 3 + 6y = 27 15 + 6y = 27 6y = 27-15 6y=12 /:6 y=2

d) 4x + 3y = -4 /* (-5) 6x + 5y = -7 /* 3 -20x - 15y = 20 18x + 15y = -21 -20x + 18x = 20 - 21 -2x = -1 /: (-2) x=1/2 4x + 3y = -4 4 * 1/2 + 3y = -4 2 + 3y = -4 3y = -4-2 3y =-6 /:3 y=-2

b) 1/2 x + y = 3 /* (-2) x - 3y = 1 -x - 2y = -6 x - 3y = 1 -2y - 3y = -6 + 1 -5y = -5 /: (-5) y=1 x- 3y = 1 x- 3 * 1 =1 x-3=1 x=1+3 x=4

zadanie 2 a) 4x - y = 8 3x + y = 6 4x + 3x = 8+6 7x = 14 /: 7 x=2 3x + y = 6 3 * 2 + y = 6 6 + y = 6 y=0

f) 2x + 3y = -4 5x + 6y =-7 3y = -4 - 2x /*2 5x + 6y = -7 6y = -8 - 4x 5x + (-8-4x) = -7 6y = -8 - 4x 5x - 8 - 4x = -7 6y = -8 - 4x 5x - 4x = -7 +8 6y = -8 - 4x x=1 6y=-8 -4 * 1 x=1 6y = -12 /:6 x=1 y=-2 x=1

e) x - 3y = 1 x+ 2y = 16 x=1+3y x+2y=16 x=1+3y 1+3y + 2y =16 x=1+3y 3y+2y=16-1 x=1+3y 5y=15 /:5 x=1+3y y=3 x=1+3 * 3 y=3 x=1+9 y=3 x=10 y=3

d) y=11-2x 5x - 4y = 8 y=11-2x 5x-4(11-2x)=8 y=11-2x 5x-44+ 8x = 8 y=11-2x 5x + 8x = 8 + 44 y=11-2x 13x=52 /: 13 y=11-2x x=4 y=11-2 * 4 x=4 y=11-8 x=4 y=3 x=4

c) x+5y=7 3x-2y=4 x=7-5y 3x-2y=4 x=7-5y 3(7-5y) - 2y = 4 x=7-5y 21 - 15y - 2y = 4 x=7-5y -15y-2y = 4- 21 x=7-5y -17y = -17 /: (-17) x=7-5y y=1 x=7-5 * 1 y=1 x=2 y=1

zadanie 1 a) x=2+y 3x -2y = 9 x=2+y 3(2+y) - 2y = 9 x=2+y 6+3y - 2y = 9 x=2+y 3y-2y=9-6 x=2+y y=3 x=2+3 y=3 x=5 y=3

poza tym nie rób zdjęcia całej stronie tylko np połowie bo potem się źle to odczytuje zrób poprawne do odczytania zdjęcia!!

pozostałych neistety nie zrobię, bo są to zdjęcia bokiem, a ja bokiem czytać niestety nie będę, popraw zdjęcia i wklej nowy link

zadanie 46 x - ilość pomarańczy w 1 skrzynce y - ilość pomarańczy w 2 skrzynce x+y=54 x-9=y+9 x+y=54 x-y=18 x+x=54+18 2x=72 /:2 x=36 x+y=54 36+y=54 y=54-36 y=18 początkowo było w jednej skrzynce 36, a w drugiej 18

zadanie 44 x - ilość chłopców y - ilość dziewcząt x+y=300 160% x = 80% y x+y=300 1,6 x = 0,8 y /: 0,8 x + y =300 2x=y x+y=300 2x-y=0 x+2x=300+0 3x=300 /:3 x=100 x+y=300 100+y=300 y=300-100 y=200 jest 200 dziewcząt i 100 chlopców