Matematyka

Rozwiąż układ równań. Dam naj...

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pschubi

a. ½(x-3) + ⅓(y+1)=1 / *6 ½(x+1) - ¼(y-1)=0 / *4 3(x-3)+2(y+1)=6 2(x+1)-(y-1)=0 3x-9+2y+2=6 2x+2-y+1=0 3x+2y=13 2x-y=-3 / *2 3x+2y=13 4x-2y=-6 / + 7x=7 / :7 x=1 3*1+2y=13 2y=10 /:2 y = 5 b. ⅓(x+1)-½(y-1)=0 / *6 ¾(x+2)-½(y+1)=1 /*4 2(x+1)-3(y-1)=0 3(x+2)-2(y+1)=1 2x+2-3y+3=0 3x+6-2y-2=1 2x-3y=-5 / *(-3) 3x-2y=5 / *2 -6x+9y=15 6x-4y=10 / + 5y=5 / :5 y=1 3x-2*1=5 3x=7 /:3 x = 2,5 c. 3/2(x-3)+2/3(y-1)=5 / *6 3/4(x-1)+4/3(y-4)=3 / *12 9(x-3)+4(y-1) = 30 9(x-1)+16(y-4)=36 9x-27+4y-4=30 9x-9+16y-64=36 9x+4y=61 / *(-1) 9x+16y=109 -9x-4y=-61 9x+16y=109 / + 12y = 48 / :12 y = 4 9x+4*4=61 9x=61-16 9x=45 / :9 x=5 d. 2/5(x+7) - 1/3(y+3)=2 / *15 1/2(x-4) + 2/3(6-y) = 3 / *6 6(x+7)-5(y+3)= 30 3(x-4)+2(6-y) = 18 6x+42-5y-15=30 3x-12+12-2y=18 6x-5y=3 3x-2y=18 / *(-2) 6x-5y=3 -6x+4y= -36 / + -y = -33 / :(-1) y = 33 3x - 2*33=18 3x = 18+66 3x = 84 / :3 x = 28

YourSweetDream

a) 1/2(x-3)+1/3(y+1)=1 1/2(x+1)-1/4(y-1)=0 1/2x-3/2+1/3y+1/3=1 1/2x+1/2-1/4y+1/4=0 1/2x+1/3y=1+3/2-1/3 1/2x-1/4y=-1/2-1/4 1/2x+1/3y=13/6 1/2x-1/4y=-3/4 /*(-1) 1/2x+1/3y=13/6 -1/2x+1/4y=3/4 7/12y=35/12 /:7/12 y=5 1/2x+1/3y=13/6 y=5 1/2x+1/3*5=13/6 y=5 1/2x+5/3=13/6 y=5 1/2x=13/6-5/3 y=5 1/2x=1/2 /:1/2 y=5 x=1 y=5 b. 1/3(x+1)-1/2(y-1)=0 3/4(x+2)-1/2(y+1)=1 1/3x+1/3-1/2y+1/2=0 3/4x+3/2-1/2y-1/2=1 1/3x-1/2y=1/3-1/2 3/4x-1/2y=1-3/2+1/2 1/3x-1/2y=-1/6 /*(-1) 3/4x-1/2y=-1 1/3x+1/2y=1/6 3/4x-1/2y=-1 13/12x=-5/6 /:13/12 x=-10/13 3/4x-1/2y=-1 x=-10/13 3/4*(-10/13)-1/2y=-1 x=-10/13 -15/26-1/2y=-1 x=-10/26 -1/2y=-1+15/26 x=-10/26 -1/2y=-11/26 /:(-1/2) x=-10/26 y=11/13 x=-10/26 c. 3/2(x-3)+2/3(y-1)=5 3/4(x-1)+4/3(y-4)=3 3/2x-9/2+2/3y-2/3=5 3/4x-3/4+4/3y-16/3=3 3/2x+2/3y=5+9/2+2/3 3/4x+4/3y=3+3/4+16/3 3/2x+2/3y=61/6 /*6 3/4x+4/3y=109/12 /*(-12) 9x+4y=61 -9x-16y=-109 -12y=-48 /:(-12) y=4 9x+4y=61 y=4 9x+4*4=61 y=4 9x+16=61 y=4 9x=61-16 x=4 9x=45 /:9 y=4 x=5 y=4 d. 2/5(x+7)-1/3(y+3)=2 1/2(x-4)+2/3(6-y)=3 2/5x+14/5-1/3y-1=2 1/2x-2+4-2/3y=3 2/5x-1/3y=2-14/5+1 1/2x-2/3y=3+2-4 2/5x-1/3y=-4/5 /*(-2) 1/2x-2/3y=1 -4/5x+2/3y=8/5 1/2x-2/3y=1 -3/10x=13/5 /:(-3/10) x=-26/3 1/2x-2/3y=1 x=-26/3 1/2*(-26/3)-2/3y=1 x=-26/3 -13/3-2/3y=1 x=-26/3 -2/3y=1+13/3 x=-26/3 -2/3y=16/3 /:(-2/3) x=-26/3 y=-8 x=-26/3

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