Zad.11/112 /-kreska ulamkowa rozwiąż układy równań: a) 3(x-1/2)+2(y+3)= 3 ½ 3x-1 /3 - y+3/ 2=-1 b)x-3/ 4 - y+5/ 2 =-1.5 x-3/ 2 - 2y-7/ 3=1 c) 2x-5/ 2 - x-6y/ 4= x+y/2 3x-1/10+2y-5/5=2x+y/2 d) x-3/5-y+1/2=1-(x-y) 4x-1/3-y-3/6=-2(x-y)

witaj:) a) 3(x-1/2)+2(y+3)= 3 ½ |*2 3x-1 /3 - y+3/ 2=-1 |*6 6x-3+4y+12=7 |*-1 6x-2-3y-9=-6 -6x-4y -9=-7 6x-3y-11=-6 dodajemy -6x-4y-9+6x-3y-11=-7+(-6) -7y=-13+11+9 -7y=7 |:-7 y=-1 podstawiam do rownania -6x-4y -9=-7 -6x=-7+9+4y -6x=2+4*(-1) -6x=2-4 -6x=-2 |:-6 x=1/3 b)x-3/ 4 - y+5/ 2 =-1.5 |*4 x-3/ 2 - 2y-7/ 3=1 |*6 x-3-2y-10=6 |*-2 3x-9-4y+14=6 -2x+6+4y+20=-12 3x-9-4y+14=6 -2x+6+4y+20+3x-9-4y+14=-12+6 x=-6-14+9-20-6 x=-25 podstawiam do rownania 3x-9-4y+14=6 3*(-25)-9-4y+14=6 -4y=6-14+9+75 -4y=76 |:-4 y=19 c) 2x-5/ 2 - x-6y/ 4= x+y/2 |*4 3x-1/10+2y-5/5=2x+y/2 |* 10 4x-10-x+6y=2x+2y 3x-1+4y-10=10x+5y 4x-x-2x-2y=10 3x+4y-10x-5y=10+1 x-2y=10 -7x-y=11 |*-2 x-2y=10 14x+2y=-22 15x=-12 x=-12/15 x=-4/5 x-2y=10 -4/5 - 2y=10 -2y=10+4/5 -2y=54/5 | * -1/2 y= - 27/5 d) x-3/5-y+1/2=1-(x-y) |*10 4x-1/3-y-3/6=-2(x-y) | 6 2x-6-5y-5=10-10x+10y 8x-2-y+3=-12x+12y 2x-5y+10x-10y=10+5+6 8x-y+12x-12y=2-3 12x-15y=21 |*-5 20x-13y=-1 |*3 -60x+75y=-105 60x-39y=-3 36y=-108 y=-3 20x-13y=-1 20x-13*(-3)=-1 20x+39=-1 20x=-40 x=-2

a)3x-3/2+2y+6=3 1/2 3x-y=-13/6 3x+2y=-1 *(-1) 3x-y=-13/6 -3x-2y=1 3x-y=-13/6 ___________ -3y=-7/6 y=-7/18 3x+7/18=-13/6 3x=-13/6-7/18 3x=-39/18-7/18 x=-46/54 b x-y=-15/10+3/4-5/2 x-2y=1+7/3+3/2 x-y=-130/40 *(-1) x-2y=29/6 -x+y=130/40 x-2y=29/6 ___________ -y=1940/240 y=-1940/240 x-2*(-1940/240)=29/6 x=-1360/120 d x-y-3/5+1/2=-x+y 4x-y-1/3-3/6=-2x+2y x-y+x-y=3/5-1/2 4x-y+2x-2y=1/3+3/6 2x-2y=1/10 *(-3) 6x-3y=5/6 -6x+6y=-3/10 6x-3y=5/6 _)______________ 3y=32/60 y=32/180 2x-2*(32/180)=1/10 2x-32/90=1/10 2x=1/10+32/90 2x=9/90+32/90 2x=41/90 x=41/80