Question

Rozwiąż układy równań metodą podstawiania.
C)
{2x-3y=-5
{-x+5y=6
D)
{3x-3y+3=0
{x+½y-2=0
E)
{4x-2y=6
{3x+6y12
F)
{3x-4y=14
{-2x+7y=-18

Answer 1

C)
{2x-3y=-5
{-x+5y=6 | *(-1)

{x=5y-6
{2(5y-6)-3y=-5
10y-12-3y=-5
7y=12-5
y=7
x= 5*7-6
{x= 29
{y=7

D)
{3x-3y+3=0
{x+½y-2=0

{x=2-½y
{3(2-½y)-3y+3=0
6-1½y-3y+3=0
6+3=4½y
y=2
x=2-½*2
{x=1
{y=2

E)
{4x-2y=6
{3x+6y=12 | /3
x+2y=4
x=4-2y
4(4-2y)-2y=6
16-10y=6
10=10y
y=1
x=4-2
{x=2
{y=1

F)
{3x-4y=14
{-2x+7y=-18 | /(-2)
x-3,5y=9
x=9+3,5y
3(9+3,5y)-4y=14
27+6,5y=14
6,5y=14-27
6,5y=-13
y=-2
x=9+3,5y*(-2)
{x=2
{y=-2

Answer 2

C)
{2x-3y=-5
{-x+5y=6

2x-3y=-5
-x=6-5y I * (-1)

2x-3y=-5
x=-6+5y

2(-6+5y)-3y=-5
x=-6+5y

-12+10y-3y=-5
x=-6+5y

10y-3y=-5+12
x=-6+5y

7y=7 /:7
x=-6+5y

y=1
x=-6+5y

y=1
x=-6+5*1

y=1
x=-6+5

y=1
x=-1

D)
{3x-3y+3=0
{x+½y-2=0

3x-3y+3=0
x=-1/2y+2

3(-1/2y+2)-3y+3=0
x=-1/2y+2

-1,5y+6-3y+3=0
x=-1/2y+2

-1,5y-3y=-6-3
x=-1/2y+2

-4,5y=-9 /:(-4,5)
x=-1/2y+2

y=2
x=-1/2*2+2

y=2
x=1


E)
{4x-2y=6
{3x+6y=12

-2y=6-4x /:(-2)
3x+6y=12

y=-3+2x
3x+6y=12

y=-3+2x
3x+6(-2+2x)=12

y=-3+2x
3x-12+12x=12

y=-3+2x
3x+12x=12+12

y=-3+2x
12x=24 /12

y=-3+2x
x=2

y=-3+2*2
x=2

y=-3+4
x=2

y=1
x=2