Rozwiązane

typ zadana-Układy równań
a)
Duza x+2y=9
Klamra y-1=3x
b)
Duza x-y=2
Klamra ½x-1=¼y
c)
Duza -x-y=2
Klamra 2(3x+y)=-20
d)
Duza 4x+3y=54
Klamra ⅓x=4(1+⅛y)

Odpowiedź :

Mirejviz
a)
{x+2y=9
{y-1=3x

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

{x + 2y = 9
{6x -2y = -2
7x = 7
x = 1 --> y = 4

b)
{x-y=2
{½x-1=¼y /*(-4)

{x - y = 2
{-2x + y = -4
-x = -2
x = 2 --> y = 0

c)
{-x-y=2
{2(3x+y)=-20

{-x - y = 2
{6x + 2y = -20 /:(-2)

{-x - y = 2
{3x + y = -10
2x = -8
x = -4 --> y = 2

d)
{4x+3y=54
{⅓x=4(1+⅛y)

{4x+3y=54
{⅓x - ½y = 4 /*6

{4x+3y=54
{2x - 3y = 24
6x = 78
x = 13 --> y = 2/3
a)
{x+2y=9
{y=3x+1

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

{x+6x+2=9
{y=3x+1

{x=1
{y=4

b)
{x=2+y
{½x-1=¼y /*4

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

{x=2+y
{4+2y=y

{x=2+y
{y=-4

{x=-2
{y=-4

c)
{-x = 2 + y
{6x+2y=-20

{x=-2-y
{6(-2-y)+2y=-20

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

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

{x=-4
{y=-2

d)
{4x+3y=54
{x=8(1+1/8y)

{4x+3y=54
{x=8+y

{4x+3y=54
{x-y=8 /*3

{4x+3y=54
{3x-3y=24 +
---------------------
7x=78
x=78/7= 11 1/7
y= 3 1/7

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