Question

Rozwiąż układ rownań metodą przeciwnych współczynników:
a)
-(x+1)-2(y+1)=-5
3x+5y=7

b)
2(x-3)+(y-5)=-4
x+2y=14

Answer 1

A)
-(x+1)-2(y+1)=-5
3x+5y=7

-x - 1 - 2y - 2 = -5
3x + 5y = 7

-x - 2y = -5 + 2 +1
3x + 5y = 7

-x - 2y = -2 |*3
3x + 5y = 7

-3x - 6y = -6
3x + 5y = 7

-y = 1 |*(-1)
y = -1

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

b)
2(x-3)+(y-5)=-4
x+2y=14

2x - 6 + y - 5 = -4
x + 2y = 14

2x + y = -4 + 6 +5
x + 2y = 14 |*(-2)

2x + y = 7
-2x - 4y = -28

-3y = -21 |:(-3)
y = 7

x + 2y = 14
x = 14 - 2*7
x = 14 - 14
x = 0

Answer 2

A)
-x-1-2y-2=-5
3x+5y=7

-x-2y=-2 |x3
3x+5y=7

-3x-6y=-6
3x+5y=7
---------------
-y=1 |x(-1)
y=-1

y=-1
3x=12 |:3

y=-1
x=4

b)
2(x-3)+(y-5)=-4
x+2y=14

2x-6+y-5=-4
x+2y=14 |x(-2)

2x+y=7
-2x-4y=-28
--------------
-3y=-21 |:(-3)
y=7

y=7
2x=7-7

y=7
x=0

Answer 3

A)
-(x+1)-2(y+1)=-5
3x+5y=7

-x-1-2y-2=-5
3x+5y=7

-x-2y=-2 /x3
3x+5y=7

-3x-6y=-6
3x+5y=7
---------------
-y=1 /x(-1)
y=-1

y=-1
3x=12 /:3

y=-1
x=4

x=4
y=-1

b)
2(x-3)+(y-5)=-4
x+2y=14

2x-6+y-5=-4
x+2y=14 /x(-2)

2x+y=7
-2x-4y=-28
--------------
-3y=-21 /:(-3)
y=7

y=7
2x=7-7

y=7
x=0

x=0
y=7