Question

Rozwiaz uklad rownan metoda podstawiania:
2x-3(x+y)+14=y-2
2(x-y)+3y +3=2y-1

Answer 1

{2x-3(x+y)=14=y-2
2(x-y)+3y+3=2y-1

2x -3x-3y-14 = y-2
2x-2y +3y +3 = 2y-1

-x -3y -y = -2 +14
2x - y -2y = -1 - 3

-x - 4y = 12 /*(-1)
2x -3y = - 4

x - 4y = - 12
2x -3y = - 4

Z pierwszego równania wyznaczam x= -12 +4y
i wstawiam do drugiego równania
x= -12 +4y
2(-12 +4y) -3y = - 4

x= -12 +4y
-24 +8y -3y = - 4

x= -12 +4y
5y = -4 +24 /:5

x= -12 +4y
y = 20:5

x= -12 +4y
y = 4

x = -12 + 4*4
y = 4

x = -12 +16
y = 4

x = 4
y = 4

Answer 2

2x-3(x+y)+14=y-2
2(x-y)+3y +3=2y-1

2x - 3x - 3y - y = -2 - 14
2x - 2y + 3y - 2y = -1 - 3

-x - 4y = -16
2x - y = -4

x = 16 - 4y
2(16-4y) - y = -4

x = 16 - 4y
32 - 9y = -4

x = 16 - 4y
9y = 4 + 32

x = 16 - 4y
y = 36/9

y = 4
x = 16 - 4 * 4

x = 0
y = 4

Answer 3

2x-3(x+y)+14=y-2
2(x-y)+3y +3=2y-1

2x-3x+3y+14=y-2
2x-2y+3y+3=2y-1

-x+3y+14=y-2
2x=2y-1+2y-3y-3

-x+3y+14=y-2
2x=y-4/:2

-x+3y+14=y-2
x=y/2-2

-(y/2-2)+3y+14=y-2
x=y/2-2

-y/2+2+3y+14=y-2
x=y/2-2

-y/2+3y-y=-2-2-14
x=y/2-2

1,5y=-18/:1.5
x=y/2-2

y=-12
x=-12/2-2

y=-12
x=-6-2

y=-12
x=-8