Zad.1 x+y =20 x-y = 10 -------- 2x = 30 /:2 x = 15 15+y = 20 y = 20-55 y =5 x=15 Od. C Zad.2 Dane jabłka : x gruszki : y x+y = 6 x = 0,5 y Odp D Zad.3 Ewelina ma czekolad : x Maciek ma : x+ 2 x+ x+2 =10 2x = 10-2 2x = 8 /:2 x = 4 czekoady Ewy Maciek = x+2 = 4+ 2 = 6 Odp. B (6,4) Zad.4 x+y+4 = 0 3x +4y+6 = 0 x+y = - 4 /* (-4) 3x +4y = -6 -4x -4y = 16 3x +4y = -6 -------------- -x = 10 / *(-1) x= - 10 -10 +y+ 4 = 0 y = 6 x = -10 Odp. C Zad. 5 Króliki : x Gęsi : y Głowy: x+y = 13 x = 13-y nogi 4x +2y = 42 Odp. B Zad. 6 Banany : x Winogron : y 3x + 5y = 26 4x +7y = 36 3x = 26-5y 4x +7y = 36 x = (26-5y)/3 4*[ (26-5y)/3] +7y = 36 /*3 x = (26-5y)/3 4(26-5y) +21y = 108 x = (26-5y)/3 104 -20y +21y = 108 x = (26-5y)/3 y = 108-104 y = 4 x = (26-5*4)/3 y = 4 x= 6/3 y=4zł x=2 zł Odp. A. 4 zł , 2 zł Zad.7 (x+y)/4 + 1 = x/2 + (13-y)/4 /*4 2(x-1) + 9 = 2 (y+1)-5 x+y + 4 = 2x +13 –y 2x – 2 + 9 = 2y + 2 -5 x+y -2x +y = 13 -4 2x -2y = 2-5-9+2 -x + 2y = 9 2x-2y = -10 --------------- x = -1 1 +2y = 9 2y = 9-1 2y =8 /:2 y = 4 X = -1 Odp. A jedno para liczb (-1 ,4) Zad. 8 Wiek córki : x Wiek matki : y x+y=46 x-10 = 2y x +y = 46 /*2 x-2y = 10 2x + 2y = 92 x-2y = 10 --------------- 3x = 102 /:3 x = 34 wiek matki 34 +y = 46 Y = 46 – 34 = 12 wiek córki za 6 lat matka : 34+6= 40 lat 46-34=12 Córka 12+6= 18 lat Odp. B . 18 lat i 40 lat Zad.9 1% = 1/100 0,75x – 66i2/3% y = 1 33 i1/3 % x+ 1/4 y = 7 3/4x – 200/3 * 1/100 y = 1 100/3 * 1/100x + 1/4y = 7 3/4x – 2/3y = 1 /*12 1/3x + 1/4y = 7 /*12 9x -8y =12 4x + 3y =84 9x = (12+8y) /:9 4x+3y = 84 x = (12+8y)/9 4[ (12+8y)/9] +3y = 84 /*9 x = (12+8y)/9 4(12+8y) + 27y = 756 x = (12+8y)/9 48 +32y +27y = 756 x = (12+8y)/9 59y = 756 -48 x = (12+8y)/9 59y = 708 /:59 x = (12+8y)/9 y = 12 x= (12+8*12)/9 y=12 x = 108/9 y = 12 x=12 y=12 Odp. D (12,12) Zad. 10 a/b = 2/5 a-7/2b = 3/20 5a = 2b 20(a-7)= 6b a = 2b/5 20a – 140 = 6b a = 2b/5 20 *2b/5 -140 = 6b a = 2b/5 8b -6b = 140 a = 2b/5 2b = 140 /:2 b = 70 a = 2*70/5 b = 70 a = 28 a+b = 28 + 70 = 98 Odp. C 98
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