Question

1.Podaj rozwiązanianastępujących układów równań:
a) 4(x-2)-(y-2)=1
10x-2y=18
b)2x-4(y+1)=10
2(x+3)-(1-y)=9

Answer 1

A)
4(x-2)-(y-2)=1
4x-8-y+2=1
(4x-y=7
(10x-2y=18

(-8x+2y=-14
(10x-2y=18
2x=4
x=2
y=1

b)
2x-4(y+1)=10
2(x+3)-(1-y)=9

(2x-4y=14
(2x+y=4

(2x-4y=14
(-2x-y=-4
-5y=10
y= -2
x= 3

Answer 2

A) 4(x-2)-(y-2)=1
10x-2y=18

4x - 8 - y + 2 = 1
10x - 2y = 18

4x - y = 1 + 8 - 2 |*(-2)
10x -2y = 18

-8x +2y = -14
10x - 2y = 18
2x = 4 |:2
x = 2

-2y = 18 - 10x
-2y = 18 - 10*2
-2y = 18 - 20
-2y - -2 |:(-2)
y = 1

b)2x-4(y+1)=10
2(x+3)-(1-y)=9

2x - 4y - 4 = 10
2x + 6 - 1 + y = 9

2x - 4y = 10+4 |*(-1)
2x + y = 9 - 6 + 1

-2x + 4y = -14
2x + y = 4

5y = -10 |:5
y = -5

2x = 4-y
2x = 4 - (-5)
2x = 4+5
2x = 9 |:2
x = 4,5

Answer 3

A)
4(x-2)-(y-2)=1
10x-2y=18

4x-8-y+2=1
10x-2y=18

4x-y=1+8
10x-2y=18

4x-y=9 /*(-2)
10x-2y=18

-8x+2y=-18
10x-2y=18

2x=0
x=0

10*0-2y=18
0-2y=18
-2y=18
y=-9

b)
2x-4(y+1)=10
2(x+3)-(1-y)=9

2x-4y-4=10
2x+6-1+y=9

2x-4y=10+4
2x+y=9-5

2x-4y=14
2x+y=4 /*(-1)

2x-4y=14
-2x-y=-4

-5y=10
y=-2

2x+(-2)=4
2x-2=4
2x=6
x=3