Question

Podaj rozwiązania nastepujących układów równań

a.2x+2y=8
2x-3y=-7

b.4y+2x=10
3x+8y=10

c.4a+2b=10
5a-2b=-10

d.5a+8b=14
4a+3b=1

e.4(x-2)-(y-2)=1
10x-2y=18

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

Answer 1

A.2x+2y=8
2x-3y=-7

2x=8-2y
8-2y-3y=-7

2x=8-2y
-5y=-15 |÷(-5)

2x=8-2y
y=3

2x=8-2*3
y=3

2x=2
y=3

x=1
y=3

b.4y+2x=10
3x+8y=10

4y=10-2x
3x+2(10-2x)=10

4y=10-2x
3x+20-4x=10

4y=10-2x
-x=-10

4y=10-2x
x=10

4y=10-2*10
x=10

4y=-10
x=10

y=-2,5
x=10

c.4a+2b=10
5a-2b=-10

a=(10-2b)÷4=2,5-½b
5(2,5-½b)-2b=-10

a=2,5-½b
12,5-2,5b-2b=-10

a=2,5-½b
-4,5b=-22,5

a=2,5-½b
b=5

a=2,5-2,5
b=5

a=0
b=5

d.5a+8b=14
4a+3b=1
--------------
a+5b=13
a=13-5b

5(13-5b)+8b=14
65-25b+8b=14
-17b=-51
b=3

a=13-5b

a=-2
b=3

e.4(x-2)-(y-2)=1
10x-2y=18

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

4x-y=7
10x-2y=18

y=4x-7
10x-2(4x-7)=18

y=4x-7
10x-8x+14=18

y=4x-7
2x=4

y=4x-7
x=2

y=4*2-7
x=2

y=1
x=2

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

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

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

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

y=4-2x
2x-16+8x=14

y=4-2x
10x=30

y=4-2x
x=3

y=4-2*3
x=3

y=-2
x=3

Answer 2

A. 2x+2y=8 I *(-1)
2x-3y=-7

-2x-2y=-8
2x-3y=-7

-5y=-15
y=3

2x+2*3=8
2x=8-6
2x=2
x=1

b.4y+2x=10 I *(-2)
3x+8y=10

-8y-4x=-20
8y+3x=10

-x=-10
x=10

4y+20=10
4y=-10
y=-10/4

c.4a+2b=10
5a-2b=-10

9a=0
a=0

2b=10
b=5

d.5a+8b=14 I * (-4)
4a+3b=1 I * 5

-20a - 32b = -56
20a+15b=5

-17b=-51
b=3

5a+24=14
5a=-10
a=-2

e.4(x-2)-(y-2)=1
10x-2y=18

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

4x-y=7 I * (-2)
10x-2y=10

-8x+2y=-14
10x-2y=10

2x=-4
x=-2

-8-y=7
-y=15
y=-15

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

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

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

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

-5y=10
5y=-10
y=-2

2x+8=10
2x=2
x=1