Question

Układy równań, 2 klasa gimnazjum str. 117 zad. 7 Skan zadania. ;) Proszę o pomoc..

Answer 1

A).
{x+2y=-2
{2x-y=1

{x=-2-2y
{2*(-2-2y)-y=1

{x=-2-2y
{-4-4y-y=1

{x=-2-2y
{-5y=1+4

{x=-2-2y
{-5y=5/:(-5)

{x=-2-2y
{y=-1

{x=-2-2*(-1)
{y=-1

{x=-2+2
{y=-1

{x=0
{y=-1

b).
{x+4y=-2
{3x-8y=10

{x=-2-4y
{3*(-2-4y)-8y=10

{x=-2-4y
{-6-12y-8y=10

{x=-2-4y
{-20y=10+6

{x=-2-4y
{-20y=16/:(-20)

{x=-2-4y
{y= -4/5

{x=-2-4*(-4/5)
{y= -4/5

{x=-2+16/5
{y= -4/5

{x=1 i 1/5
{y= -4/5

c).
{x-2y=3
{-2x+y=0

{x=3+2y
{-2*(3+2y)+y=0

{x=3+2y
{-6-4y+y=0

{x=3+2y
{-3y=6/:(-30

{x=3+2y
{y=-2

{x=3+2*(-2)
{y=-2

{x=3-4
{y=-2

{x=-1
{y=-2

d).
{2x+y=9
{5x-4y=3

{y=9-2x
{5x-4*(9-2x)=3

{y=9-2x
{5x-36+8x=3

{y=9-2x
{13x=3+36

{y=9-2x
{13x=39/:13

{y=9-2x
{x=3

{y=9-2*3
{x=3

{y=3
{x=3

e).
{3x-2y=5
{2x-y=4

{3x-2y=5
{-y=4-2x/*(-1)

{3x-2y=5
{y=-4+2x

{3x-2*(-4+2x)=5
{y=-4+2x

{3x+8-4x=5
{y=-4+2x

{-x=5-8
{y=-4+2x

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

{x=3
{y=-4+2*3

{x=3
{y=-4+6

{x=3
{y=2

f).
{2x+9y=-9
{-3x+3y=8 /:(-3)

{2x+9y=-9
{x-y=-8/3

{2x+9y=-9
{x= -8/3+y

{2*(-8/3+y)+9y=-9
{x= -8/3+y

{-16/3+2y+9y=-9
{x= -8/3+y

{11y= -9+16/3
{x= -8/3+y

{11y= -3 i 2/3 /:11
{x= -8/3+y

{y= -11/3*1/11
{x= -8/3+y

{y= -1/3
{x= -8/3-1/3

{y= -1/3
{x= -3

g).
{2x+3y=4 /:2
{8x-5y=-1

{x+3/2y=2
{8x-5y=-1

{x=2-3/2 y
{8*(2-3/2 y)-5y=-1

{x=2-3/2 y
{16-12y-5y=-1

{x=2-3/2 y
{-17y=-1-16

{x=2-3/2 y
{-17y=-17/:(-17)

{x=2-3/2 y
{y=1

{x=2-3/2*1
{y=1

{x=2-3/2
{y=1

{x=1/2
{y=1

h).
{x-y=0
{x+y+z=4
{x+2y+3z=9

{-y=-x/*(-1)
{y=x
{x+x+z=4
{x+2*x+3z=9

{y=x
{2x+z=4
{x+2x+3z=9

{y=x
{z=4-2x
{3x+3*(4-2x)=9

{y=x
{z=4-2x
{3x+12-6x=9

{y=x
{z=4-2x
{-3x=9-12

{y=x
{z=4-2x
{-3x= -3/:(-3)

{y=x
{z=4-2x
{x=1

{y=x
{z=4-2*1
{x=1

{y=1
{z=2
{x=1

{x=1
{y=1
{z=2