Zad.8 TYLKO PRZYKŁAD C I D ZAD.9 WZORY SKRÓCONEGO MNOŻENIA

c) {x+y/2+2x+y/3=4 /*6 {2x-y/4-x+y/6=-¹/₆ /*12 ułamki sie skracają [3x+3y+4x+2y=24 [6x-3y-2x-2y=-2 {7x+5y=24 {4x-5y=-2 ~~~~~~~~~~~~ 11x=22/:11 __x=2 7x+5y=24 7*2+5y=24 14+5y=24 5y=24-14 5y=10/:5 y=2 rozwiązanie to {x=2 {y=2 d) {2x-y/3+x+2y/6=-2½ {2x+y/4-2x-y/2=1½ [2x-y/3+x+2y/6=-⁵/₂ /*6 [2x+y/4-2x-y/2=³/₂ /*4 {4x-2y+x+2y=-15 {2x+y-4x+2y=6 [5x=-15/:5 [-2x+3y=6 {x=-3 {-2*(-3)+3y=6 [x=-3 [6+3y=6 {x=-3___________________{x=-3 {3y=0/:3________________{y=0 a) zad 9 {(x-5)²+x(3-x)+5y=-1 {(y-3)²+(5-y)(5+y)+x=6 [x²-10x+25+3x-x²+5y=-1 [y²-6y+9+25+5y-5y-y²+x=6 {-7x+5y=-26 {x-6y=-28/*7 [-7x+5y=-26 [7x-42y=-196 ``````````````` ____-37y=-222/(-37) _______y=6 -7x+5y=-26 -7x+5*6=-26 -7x+30=-26 -7x=-56/:(-7) ___x=8 __________________{x=8___{y=6 b) {(x+2)²-(x-3)(x+3)-2y=-1 {(y-8)²-(y-10)²+3x=14 [x²+4x+4-(x²+3x-3x-9)-2y=-1 [y²-16y+64-(y²-20y+100)+3x=14 {x²+4x+4-x²-3x+3x+9-2y=-1 {y²-16y+64-y²+20y-100+3x=14 [4x-2y=-14/*2 [3x+4y=50 {8x-4y=-28 {3x+4y=50 ~~~~~~~~~~~~ 11x=22/:11 ___x=2 8x-4y=-28 8*2-4y=-28 16-4y=-28 -4y=-28-16 -4y=-44/:(-4) ___y=11 c) {(4-x)²-x(x-3)+4y=-7 {(y+1)²+y(5-y)-3x=1 [16-8x+x²-x²+3x+4y=-7 [y²+2y+1+5y-y²-3x=1 {-5x+4y=-23/*3 {-3x+7y=0/*(-5) [-15x+12y=-69 [15x-35y=0 ```````````` _____-23y=-69/:(-23) ________y=3 -5x+4y=-23 -5x+4*3=-23 -5x+12=-23 -5x=-35/:(-5) __x=7 d) {(x-8)²-(x-9)²=2y-7 {(y+1)²-(y-3)(y+3)=3x-6 [x²-16x+64-(x²-18x+81)=2y-7 [y²+2y+1-(y²+3y-3y-9)=3x-6 {x²-16x+64-x²+18x-81=2y-7 {y²+2y+1-y²-3y+3y+9=3x-6 [2x-2y=10 [-3x+2y=-7 `````````` ___-x=3/*(-1)______x=3 2x-2y=10 2*3-2y=10 6-2y=10 -2y=4/:(-2) __y=-2

c) (4-x)2 - x(x-3) + 4y = - 7 (y+1)2 + y(5-y) - 3x = 1 16 - 8x + x2 - x2 + 3x + 4y = -7 y2 + 2y + 1 + 5y - y2 - 3x = 1 -5x + 4y = -23 -3x + 7y = 0 /: 3 -5x + 4y = -23 -x = - 7/3 y /: (-1) -5x + 4y = -23 x= 7/3y -5(7/3y) + 4y = -23 x= 7/3y -35/3y + 4y = -23 x= 7/3y -39/3y = -23 /:(-1) x= 7/3y 39/3y =23 x= 7/3y y= 13/23 x = 91/69 d) (x-8)2 - (x-9)2 = 2y - 7 (y+1)2 - (y -3 )(y+3) = 3x - 6 x2 - 16x + 64 - ( x2 - 18x + 81) = 2y - 7 y2 + 2y + 1 - ( y2 + 3y - 3y - 9) = 3x - 6 x2 - 16x + 64 - x2 + 18x - 81 = 2y - 7 y2 + 2y + 1 - y2 - 3y + 3y + 9 = 3x - 6 2x - 2y = 10 / : 2 -3x + 2y = -16 x - y = 5 -3x + 2y = -16 x= 5 + y -3(5 + y) + 2y = -16 x= 5 + y -15 - 3y + 2y = -16 x= 5 + y -1y = -1 x= 5 + y y = 1 x = 6