Rozwiązane

Rozwiąż układy równań metodą podstawiania
a) ( x+y=5
( x-2y=-1

b) (y-x=4
(3(x+y)=24

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

d) (3x-1=y-2
(4x-3=-2(y-2)

e) (x+2y=9
(y-1=3x

f) (x-y=2
(½x-1=¼y

Prosił bym o pomoc .Pozdrawiam i z góry dziękuje (te nawiasy na poczatku to sa lczniki łaczące te 2 równania )

Odpowiedź :

Matimenviz
A) x=5-y
5-y-2y=-1
x=5-y
-3y=-6/:-3
y=2
x=5-2
x=3
B)
y=4+x
3(x+4+x)=24
y+4+x
3x+12+3x=24
6x=12/:6
x=2
y=6
c)
x=4+2y
4+2y+3=2y
2y-2y=-7
0=-7

Sylwusia2viz
a)(x=5-y
(x-2y=-1

(x=5-y
(5-y-2y=-1

(x=5-y
(5-3y=-1/-5

(x=5-y
(-3y=-6/(-3)

(x=5-y
(y=2

(x=5-2
(y=2

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

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

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

{x=5-y
{-3y=-1-5

{x=5-y
{-3y=-6 / : (-3)

{x=5-y
{y=2

{x=5-2
{y=2

{x=3
{y=2

B)
{y-x=4
{3(x+y)=24

{y=4+x
{3(x+y)=24

{y=4+x
{3(x+4+x)=24

{y=4+x
{3x+12+3x=24

{y=4+x
{6x=24-12

{y=4+x
{6x=12 / :6

{y=4+x
{x=2

{y=4+2
{x=2

{y=6
{x=2

C)
{x-2y=4
{x+3=2y

{x-4=2y
{x+3=2y
---------------
2x-1=0
2x=1 /:2
x=½

x+3=2y
½+3=2y
3½=2y /:2
1¾=y

D)
{3x-1=y-2
{4x-3=-2(y-2)

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

{3x-1+2=y
{4x-3=-2y+4

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

{3x-1+2=y
{4x-3=-6x+2-4+4

{3x-1+2=y
{4x+6x=2+3

{3x-1+2=y
{10x=5 /:10

{3x-1+2=y
{x=½

{1½-1+2=y
{x=½

{2½=y
{x=½

E)
{x+2y=9
{y-1=3x

{x+2y=9
{y=3x+1

{x+2(2x+1)=9
{y=3x+1

{x+4x+2=9
{y=3x+1

{x+4x=9-2
{y=3x+1

{5x=7 /:5
{y=3x+1

{x=⅕
{y=1⅗
f)
{x-y=2
{½x-1=¼y

{x=2+y
{½(2+y)-1=¼y

{x-y=2
{1+½y-1=¼y

{x-y=2
{½y-¼y=1-1

{x-y=2
{y=0

{x=2
{y=0

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