Rozwiąż podane układu równań metoda podstawiania . Na dzisaj pilne!!!
a){ x-2y=3
{ -2x + y=0
b) { 2×+ y=9
{ 5× - 4y=3
c) { 3× ₋2y=5
{ 2×₋y=4
d) { 2×₊ 9y= ⁻9
{ -3×₊3y=8
e) { 2×₊3y=4
{ 8×₋5y=-1
f) { x₋y=0
{ x₊y₊z=4
{ x₊2y₊3z=9

3

Odpowiedzi

2009-12-08T14:42:04+01:00
A)
x - 2y = 3
x = 3 + 2y
-2x + y = 0
-2( 3 + 2y) + y = 0
-6 - 4y + y = 0
-3y = 6 //: -3
y = -2
x = 3 + (-4)
x = -1
B) 2x + y =9
y = 9 - 2x
5x - 4y = 3
5x - 4(9-2x) = 3
5x - 36 + 2x = 3
7x = 39
x = 5,(571428)
y = 9 - 2
c) 2x - y = 4
-y = 2x - 4
y = -2x + 4
3x - 2y = 5
3x - 2(-2x +4) =5
3x + 4x -8=5
7x = 13
x=1,(857142)



2009-12-08T14:43:18+01:00
A) { 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 /:-3

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

b) { 2×+ y=9
{ 5× - 4y=3

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

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

{13x = 39
x=3
y=9-6=3

c) { 3× ₋2y=5
{ 2×₋y=4

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

3x - 2(2x-4)=5
3x - 4x + 8 = 5
-x = -3
x = 3
y = 6-4=2

d) { 2×₊ 9y= ⁻9
{ -3×₊3y=8 /:3

-x+y=8/3
y=8/3 + x

2x + 9(8/3 + x) = -9
2x + 24 + 9x = -9
11x = -33
x = -3
y=-1/3

e) { 2×₊3y=4 /:2
{ 8×₋5y=-1

x = 2 - 3/2y
8(2-3/2y) - 5y = -1
16 - 12y - 5y = -1
-17y = - 17
y=1
x=2-1,5=0,5

f) { x₋y=0
{ x₊y₊z=4
{ x₊2y₊3z=9

x=y
z=4-x-y
x+2y+12-3x-3y=9
y+2y+12-3y-3y=9
-3y=-3
y=1
x=1
z=4-1-1=2
Najlepsza Odpowiedź!
2009-12-08T15:37:33+01:00
A){ x-2y=3
{ -2x + y=0

{x=3+2y
{-2x + y=0
-2×(3+2y)+y=0
-6-4y+y=0
-6-3y=0
-3y=6/÷(-3)
y=-2
x=3+2y
x=3+2×(-2)
x=3-4
x=-1
{x=-1
{y=-2

b) { 2×+ y=9
{ 5× - 4y=3

{ y=9-2x
{5x-4(9-2x)=3
5x-36+8x=3
5x+8x=3+36
13x=39/÷13
x=3
y=9-2x
y=9-2×3
y=9-6
y=3
{x=3
{y=3

c) { 3× ₋2y=5
{ 2×₋y=4
-y=4-2x/×(-1)
y=-4+2x
3x-2×(-4+2x)=5
3x+8-4x=5
-x=5-8
-x=-3/×(-1)
x=3
y=-4+2x
y=-4+2×3
y=-4+6
y=2
{x=3
{y=2

d) { 2×₊ 9y= ⁻9
{ -3×₊3y=8
2x=-9-9y/÷ 2
x=-⁹/₂-⁹/₂y
-3×(-⁹/₂-⁹/₂y)+3y=8
²⁷/₂+²⁷/₂y+3y=8
²⁷/₂+²⁷/₂y+⁶/₂y=8
³³/₂y=8-²⁷/₂
³³/₂y=¹⁶/₂-²⁷/₂
³³/₂y=-¹¹/₂/÷³³/₂
y=-⅓
x=-⁹/₂-⁹/₂×(-⅓)
x=-⁹/₂+³/₂
x=-⁶/₂
x=-3
{x=-3
{y=-⅓


e) { 2×₊3y=4
{ 8×₋5y=-1
2x=4-3y/÷ 2
x=2-³/₂y
8×₋5y=-1
-5y=-1-8x
-5y=-1-8×(2-³/₂y)
-5y=-1-16+²⁴/₂y
-5y=-17+12y
-15y-12y=-17
-17y=-17/÷(-17)
y=1
x=2-³/₂y
x=2-³/₂×1
x=2-³/₂
x=½
y=1

f) { x₋y=0
{ x₊y₊z=4
{ x₊2y₊3z=9

x=y
podstawiam y za x w drugim równaniu y+y+z=4
2y=4-z/÷2
y=2-z/2
w trzecim rownaniu za y podstawiam 2-z/2, a za x y
x₊2y₊3z=9
y+2(2-z/2)+3z=9
y+4-2z/2+3z=9
y+4-z+3z=9
y+4+2z=9
y+2z=9-4 znowu za y podstawiam 2-z/2
2-z/2+2z=5/×2 mnożąc przez 2, pozbywam sie mianownika
4-z+4z=10
3z=10-4
3z=6/÷3
z=2
teraz y
y=2-z/2
y=2-²/₂ za z w liczniku podstawiam 2
y=2-1
y=1
y=x
{x=1
{y=1
{z=2

2 3 2