Rozwiązane

Rozwiaz uklady rownan?
a) x+2y=9
y-1=3x
b) x-y=2
1/2x - 1=1/4y
c) -x-y=2
2 (3x+y)= -20
d) 4x+3y=54
1/3x=4(1+1/8y)

Odpowiedź :

a)

x+2y=9
y-1=3x

x+2y=9
y=3x+1

x+2(3x+1)=9
y= 3x+1

x+6x+2=9
y=3x+1

7x=9-2
y=3x+1

7x=7 /7
y=3x+1

x=1
y=4



b)

x-y=2
1/2x-1= 1/4y

x=2+y
1/2(2+y)-1=1/4y

x=2+y
1+ 1/2y -1 = 1/4y

x=2+y
1-1=1/4y-1/2y

x= 2+y
1/2y=0

x=2
y=0



c)

-x-y=2
2(3x+y) = - 20

-x-y=2
6x+2y=-20

-x=2+y / -1
6x+2y=-20

x= -2-y
6(-2-y)+2y=-20

x=-2-y
-12-6y+2y=-20

x=-2-y
-4y=-20+12 /-4

x=-2-y
y=2

x=-4
y=2



d)

4x+3y=54
1/3x=4(1+1/8y)

3y=54-4x /3
1/3x=4(1=1/8y)

y=18-4/3x
1/3x=4(1+1/8(18-4/3x))

y=18-4/3x
1/3x=4+9-4/6x

y=18-4/3x
1/3x+4/6x=4+9

y=18-4/3x
2/6x+4/6x=13

y=18-4/3x
x=13

y=18-4/3 *13
x=13

y= 18- 52/3
x=13

y= 18- 17 i1/3
x=13

y=2/3
x=13
a) x + 2y = 9
y - 1 = 3x

x = 9 - 2y /-2y
y = 3x + 1 /+1

x = 9 - 2(3x + 1) = 9 - 6x - 2 /+6x
y = 3x + 1

7x = 7 czyli x = 1
y = 3 * 1 + 1 = 3 + 1 = 4


b)x - y = 2 /+y
1/2x - 1 = 1/4y /*4

x = 2 - y
2x - 4 = y

x = 2 - 2x + 4 = 6 - 2x /+2x
y = 2x - 4

3x = 6 /:3 czyli x = 2
y = 2 * 2 - 4 = 0


c) -x-y=2 /*(-1)
2(3x+y)=-20

x+y=-2 /-y
6x+2y=-20 /-6x /:2

x=-2-y
y=-10-3x

x=-2+10+3x=8+3x /-3x
y=-10-3x

-2x=8 czyli x=-4
y=-10-3*(-4)=-10+12=2


d)4x+3y=54
1/3x=4(1+1/8y)

4x+3y=54
1/3x=4+1/2y /*6

4x+3y=54
2x=24+3y /-3y

4x+3y=54
+ 2x-3y=24

6x=78
x=78/6=13

4*13+3y=54
52 + 3y = 54 /-52
3y=3 /:3
y=1
a) x+2y=9/*3
-3x+y=1

3x+6y=27
-3x+y=1

y=4
x=1

B) 1/2 x-1/4 y =1/*(-2)
x-y=2

-x+1/2 y = -2
x-y=2

y=0
x=2

c) -x-y=2/*2
6x+2y=-20

-2x-2y=4
6x+2y=-20

x=-4
y=2

d) 1/3 x - 1/2 y =4/*6
4x +3y =54

2x-3y=24
4x+3y=54

x=13
y=2/3

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