. a) x+5/3-(1-y)=-3 |*3 y+5/2-(x-1)=4 |*2 3x+5-3+3y=-9 |-2 2y+5-2x+2=8 |-7 3x+3y=-11 |*2 2y-2x=1 |*3 6x+6y=-22 6y-6x=3 12y=-19 |/12 y=-19/12 3x+3y=-11 3x+3(-19/12)=-11 3x-19/4=-11 |+19/4 3x=-11+19/4 3x=-25/4 |/3 x=-25/12 ODP: x=-²⁵/₁₂ y=-¹⁹/₁₂ . b) x-1/4+2=y |-2, +1/4 y-3/3+5=x |-5, +1 x-y=-7/4 y-x=-4 0=-23/4 ODP: To nie jest równanie. . c) x+5/2+2y-1/3=4 |*6 3x+1/2+5y+2/4=5 |*2 6x+15+12y-2=24 6x+1+10y+1=10 12y+6x+13=24 |-13 10y+6x+2=10 |-2 12y+6x=11 10y+6x=8 |/-1 12y+6x=11 -10y-6x=-8 2y=3 y=3/2 10y+6x=8 10(3/2)+6x=8 15+6x=8 |-15 6x=-7 |/6 x=-7/6 ODP: x=-⁷/₆ y=³/₂ . d) x+6/3+3y+1/2=5 |*6 y+1/2+x+5/8=2 |*8 6x+12+18y+3=30 8y+4+8x+5=16 18y+6x+15=30 |-15 8y+8x+9=16 |-9 18y+6x=15 8y+8x=7 |-8y 8x=7-8y |/8 x=7/8-y 18y+6(7/8-y)=15 18y-6y+21/4=15 |-21/4 12y=15-21/4 12y=39/4 |/12 y=13/6 ODP: x=¹/₁₆ y=¹³/₁₆ . e) x+2/2-y-2/4=3 |*2 x-2/2-3y+1/7=0 |*7 2x+2-2y-1=3 |+1,-2 7x-7-21y+1=0 |+7,-1 2x-2y=5 7x-21y=6 |/7 2x-2y=5 x-3y=6/7 2x-2y=5 x=6/7+3y 2(6/7+3y)-2y=5 x=6/7+3y 12/7+4y=5 |-(12/7), /4 x=6/7+3y y=(5-12/7)/4 x=6/7+3y y=23/28 x=6/7+3y y=23/28 x=6/7+3(23/28) y=23/28 x=6/7+69/28 y=23/28 x=93/28 ODP: x=⁹³/₂₈ y=²³/₂₈
a)x+5/3-(1-y)=-3 y+5/2-(x-1)=4 x+5/3-1+y=-3 y+5/2-x+1=4 + -------------------------- 2y+5/3+5/2+1=1 /-31/6 2y=(-25/6) /:2 y=(-25/12)=(-2i1/12) x+5/3-(1-(-25/12))=-3 x+5/3-27/12=-3 /+7/12 x=(-2i5/12)
a) x+5/3-(1-y)=-3 y+5/2-(x-1)=4 x+y= -3-5/3+1 -x+y= 4-5/2-1 x+y= -3 i 2/3 -x+y= 1/2 x= -11/3-y -(-11/3-y) +y =1/2 x= -11/3-y 11/3+y+y= 1/2 x= -11/3-y 2y= 1/2 - 11/3 x= -11/3-y 2y= 3/6 -22/6 x= -11/3-y 2y= -19/6 x= -11/3-y y= -11/6 * 1/2 x= -11/3-y y= -11/12 x= -11/3 - (-11/12)= -44/12 + 11/12 = - 33/12 x= -33/12 y= -11/12 ( można wydzielać całości, ale do sprawdzenia chyba lepiej zostawić w ułamkach) b) x-1/4+2=y y-3/3+5=x x-y= -2+1/4 -x +y = -5 +3/3 x-y= -7/4 -x+y = - 4 (3/3 to jedna całość) x= - 7/4 +y -(- 7/4 +y) +y = -4 x= - 7/4 +y 7/4 - y +y= -4 x= - 7/4 +y 0 = - 4 -7/4 ( nie ma tu pomyłki w tekście zadania? albo układ równań nie ma rozwiązań) c) x+5/2+2y-1/3=4 3x+1/2+5y+2/4=5 x+2y = 4 -5/2 +1/3 3x+5y = 5 -1/2-2/4 x+2y= 4- 15/6 + 2/6 3x+5y= 5-2/4 -2/4 x+2y = 4-13/6 3x+5y= 5-1 x+2y= 11/6 3x+5y= 4 x= 11/6-2y 3*(11/6-2y) +5y =4 x= 11/6-2y 33/6 - 6y + 5y = 4 x= 11/6-2y -y= 4- 33/6 x= 11/6-2y -y= -9/6 x= 11/6-2y y= 3/2 x= 11/6 - 2* 3/2= 11/6 -3= - 7/6 x= -7/6 y=3/2 d) x+6/3+3y+1/2=5 y+1/2+x+5/8=2 x+3y =5 -2 -1/2 x+y= 2 -1/2-5/8 x+3y= 2 i 1/2 x+y= 2-9/8 x+3y= 5/2 x+y= 9/8 x= 5/2 - 3y 5/2 - 3y +y=9/8 x= 5/2 - 3y -2y= 9/8 - 20/8 x= 5/2 - 3y -2y= -11/8 / (-1) x= 5/2 - 3y y= 11/8 * 1/2 x= 5/2 - 3y y= 11/16 x= 5/2 - 3* 11/16= 5/2 - 33/16 = 40/16-33/16= 7/16 x=7/16 y=11/16 e) x+2/2-y-2/4=3 x-2/2-3y+1/7=0 x-y= 3 - 1 +2/4 x-3y= 1 - 1/7 x-y= 2 i 2/4 x-3y= 6/7 x-y =10/4 x-3y= 6/7 x= 10/4 +y x-3y= 6/7 x= 10/4 +y 10/4 +y -3y=6/7 x= 10/4 +y - 2y = 6/7 - 10/4 x= 10/4 +y -2y= 24/28 - 70/28 x= 10/4 +y -2y= - 46/28 /*(-1) x= 10/4 +y y= 46/56 x= 10/4 +y y= 23/28 x= 10/4 +23/28= 70/28 + 23/28= 93/28 x=93/28 y=23/28
Rozwiąż układ równań: 1/2x + 1/4y = 0,25 -3/4x - 1/2y = 0,5 Potrzebne jeszcze na dziś, dam naj za poprawny wynik PS: na poziomie 6 klasy, z góry dzięki ...
