Hej mam do rozwiązania 10przykłądów z układów równań prosze o rozwiązanie,kompletnie tego nie rozumiem.Daje sporo punktów wiec się opłaca;)TYLKO PROSZE NIE PISAĆ SAMYCH WYNIKOW TYLKO OBLICZENIA I WYNIK.
Rozwiąż układy równań:
7.
a){2x-y=-1
{3x+2y=9
b){2y-x=8
{4x+3y=1
c){3x-8y=8
{2x-y=1
d){2x+3y=20
{-x+3y=-1
4.
a){x+y=2
{x-y=1
b){2x+y=5
{4x-y=10
c){3x+2y=2
{3x+y=1i1/2
d){x+y=0
{2x+4y=1
e){3x-2y=3
{3x+y=1i1/2
f){x+2y=-1/2
{3x+4y=-1
Rozwiąż układy równań:
7.
a){2x-y=-1
{3x+2y=9
b){2y-x=8
{4x+3y=1
c){3x-8y=8
{2x-y=1
d){2x+3y=20
{-x+3y=-1
4.
a){x+y=2
{x-y=1
b){2x+y=5
{4x-y=10
c){3x+2y=2
{3x+y=1i1/2
d){x+y=0
{2x+4y=1
e){3x-2y=3
{3x+y=1i1/2
f){x+2y=-1/2
{3x+4y=-1
od Ewe622
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Odpowiedzi
A){2x-y=-1 I*2
{3x+2y=9
4x-2y=-2
3x+2y=9
________
7x=7
x=1
3*1+2y=9
3+2y=9
2y=6
y=3
x=1
y=3
b){2y-x=8
{4x+3y=1
-x+2y=8 I*4
4x+3y=1
-4x+8y=32
4x+3y=1
__________
11y=33
y=3
-x+2*3=8
-x+6=8
-x=2
x=-2
x=-2
y=3
c){3x-8y=8
{2x-y=1 I*(-8)
3x-8y=8
-16x+8y=-8
___________
-15x=0
x=0
3*0-8y=8
0-8y=8
-8y=8
y=-1
x=0
y=-1
d){2x+3y=20
{-x+3y=-1 I*(-1)
2x+3y=20
x-3y=1
_____________
3x=21
x=7
7-3y=1
-3y=-6
y=2
x=7
y=2
4.
a){x+y=2
{x-y=1
__________
2x=3
x=1½
1½-y=1
-y=-½
y=½
x=1½
y=½
b){2x+y=5
{4x-y=10
___________
6x=15
x=2½
2*2½+y=5
5+y=5
y=0
x=2½
y=0
c){3x+2y=2 I*(-1)
{3x+y=1½
-3x-2y=-2
3x+y=1½
_____________
-y=-½
y=½
3x+½=1½
3x=1
x=⅓
x=⅓
y=½
d){x+y=0 I*(-2)
{2x+4y=1
-2x-2y=0
2x+4y=1
___________
2y=1
y=½
x+½=0
x=-½
x=-½
y=½
e){3x-2y=3 I*(-1)
{3x+y=1½
-3x+2y=-3
3x+y=1½
__________
3y=1½
y=½
3x+½=1½
3x=1
x=⅓
x=⅓
y=½
f){x+2y=-½ I*(-2)
{3x+4y=-1
-2x-4y=1
3x+4y=-1
___________
x=0
3*0+4y=-1
4y=-1
y=-¼
x=0
y=-¼
Pozdro ;*
{3x+2y=9
4x-2y=-2
3x+2y=9
________
7x=7
x=1
3*1+2y=9
3+2y=9
2y=6
y=3
x=1
y=3
b){2y-x=8
{4x+3y=1
-x+2y=8 I*4
4x+3y=1
-4x+8y=32
4x+3y=1
__________
11y=33
y=3
-x+2*3=8
-x+6=8
-x=2
x=-2
x=-2
y=3
c){3x-8y=8
{2x-y=1 I*(-8)
3x-8y=8
-16x+8y=-8
___________
-15x=0
x=0
3*0-8y=8
0-8y=8
-8y=8
y=-1
x=0
y=-1
d){2x+3y=20
{-x+3y=-1 I*(-1)
2x+3y=20
x-3y=1
_____________
3x=21
x=7
7-3y=1
-3y=-6
y=2
x=7
y=2
4.
a){x+y=2
{x-y=1
__________
2x=3
x=1½
1½-y=1
-y=-½
y=½
x=1½
y=½
b){2x+y=5
{4x-y=10
___________
6x=15
x=2½
2*2½+y=5
5+y=5
y=0
x=2½
y=0
c){3x+2y=2 I*(-1)
{3x+y=1½
-3x-2y=-2
3x+y=1½
_____________
-y=-½
y=½
3x+½=1½
3x=1
x=⅓
x=⅓
y=½
d){x+y=0 I*(-2)
{2x+4y=1
-2x-2y=0
2x+4y=1
___________
2y=1
y=½
x+½=0
x=-½
x=-½
y=½
e){3x-2y=3 I*(-1)
{3x+y=1½
-3x+2y=-3
3x+y=1½
__________
3y=1½
y=½
3x+½=1½
3x=1
x=⅓
x=⅓
y=½
f){x+2y=-½ I*(-2)
{3x+4y=-1
-2x-4y=1
3x+4y=-1
___________
x=0
3*0+4y=-1
4y=-1
y=-¼
x=0
y=-¼
Pozdro ;*
7. a) {2x-y=-1
{3x+2y=9
{-y=-1-2x/:(-1)
{3x+2y=9
{y=1+2x
{3x+2*(1+2x)=9
{y=1+2x
{3x+2+4x=9
{y=1+2x
{7x=7/:7
{y=1+2x
{x=1
{y=3
{x=1
b){2y-x=8
{4x+3y=1
{-x=8-2y/:(-1)
{4x+3y=1
{x=-8+2y
{4*(-8+2y)+3y=1
{x=-8+2y
{-32+8y+3y=1
{x=-8+2y
{11y=33/:11
{x=-8+2y
{y=3
{x=-8+2*6
{y=3
{x=4
{y=3
c) {3x-8y=8
{2x-y=1
{3x-8y=8
{-y=1-2x/:(-1)
{3x-8y=8
{y=-1+2x
{3x-8*(-1+2x)=8
{y=-1+2x
{3x+8-16x=8
{y=-1+2x
{-13x=0/:(-13)
{y=-1+2x
{x=0
{y=-1+2*0
{x=0
{y=-1
d) {2x+3y=20
{-x+3y=-1
{2x+3y=20
{-x=-1-3y/:(-1)
{2x+3y=20
{x=1+3y
{2*(1+3y)+3y=20
{x=1+3y
{2+6y+3y=20
{x=1+3y
{9y=18/:9
{x=1+3y
{y=2
{x=1+3*2
{y=2
{x=7
4. a) {x+y=2
{x-y=1
{x+y=2
{x=1+y
{1+y+y=2
{x=1+y
{2y=1/:2
{x=1+y
{y=½
{x=1+½
{y=½
{x=1½
b) {2x+y=5
{4x-y=10
{y=5-2x
{4x-(5-2x)=10
{y=5-2x
{4x-5+2x=10
{y=5-2x
{6x=15/:6
{y=5-2x
{x=2½
{y=5-2*2½
{x=2½
{y=0
{x=2½
c) {3x+2y=2
{3x+y=1½
{3x+2y=2
{y=1½-3x
{3x+2*(1½-3x)=2
{y=1½-3x
{3x+3-6x=2
{y=1½-3x
{-3x=-1/:(-3)
{y=1½-3x
{x=⅓
{y=1½-3*(⅓)
{x=⅓
{y=½
d){x+y=0
{2x+4y=1
{x=-y
{2*(-y)+4y=1
{x=-y
{2y=1/:2
{x=-y
{y=½
{x=-½
{y=½
e) {3x-2y=3
{3x+y=1½
{3x-2y=3
{y=1½-3x
{3x-2*(1½-3x)=3
{y=1½-3x
{3x-5+6x=3
{y=1½-3x
{9x=8/:9
{y=1½-3x
{x=⁸/₉
{y=1½-3*(⁸/₉)
{x=⁸/₉
{y=1½-2⅔
{x=⁸/₉
{y=-⁵/₆
f) {x+2y=-½
{3x+4y=-1
{x=-½-2y
{3*(-½-2y)+4y=-1
{x=-½-2y
{-³/₂-6y+4y=-1
{x=-½-2y
{-2y=½/:(-2)
{x=-½-2y
{y=-¼
{x=-½-2*(-¼)
{y=-¼
{x=0
{y=-¼
{3x+2y=9
{-y=-1-2x/:(-1)
{3x+2y=9
{y=1+2x
{3x+2*(1+2x)=9
{y=1+2x
{3x+2+4x=9
{y=1+2x
{7x=7/:7
{y=1+2x
{x=1
{y=3
{x=1
b){2y-x=8
{4x+3y=1
{-x=8-2y/:(-1)
{4x+3y=1
{x=-8+2y
{4*(-8+2y)+3y=1
{x=-8+2y
{-32+8y+3y=1
{x=-8+2y
{11y=33/:11
{x=-8+2y
{y=3
{x=-8+2*6
{y=3
{x=4
{y=3
c) {3x-8y=8
{2x-y=1
{3x-8y=8
{-y=1-2x/:(-1)
{3x-8y=8
{y=-1+2x
{3x-8*(-1+2x)=8
{y=-1+2x
{3x+8-16x=8
{y=-1+2x
{-13x=0/:(-13)
{y=-1+2x
{x=0
{y=-1+2*0
{x=0
{y=-1
d) {2x+3y=20
{-x+3y=-1
{2x+3y=20
{-x=-1-3y/:(-1)
{2x+3y=20
{x=1+3y
{2*(1+3y)+3y=20
{x=1+3y
{2+6y+3y=20
{x=1+3y
{9y=18/:9
{x=1+3y
{y=2
{x=1+3*2
{y=2
{x=7
4. a) {x+y=2
{x-y=1
{x+y=2
{x=1+y
{1+y+y=2
{x=1+y
{2y=1/:2
{x=1+y
{y=½
{x=1+½
{y=½
{x=1½
b) {2x+y=5
{4x-y=10
{y=5-2x
{4x-(5-2x)=10
{y=5-2x
{4x-5+2x=10
{y=5-2x
{6x=15/:6
{y=5-2x
{x=2½
{y=5-2*2½
{x=2½
{y=0
{x=2½
c) {3x+2y=2
{3x+y=1½
{3x+2y=2
{y=1½-3x
{3x+2*(1½-3x)=2
{y=1½-3x
{3x+3-6x=2
{y=1½-3x
{-3x=-1/:(-3)
{y=1½-3x
{x=⅓
{y=1½-3*(⅓)
{x=⅓
{y=½
d){x+y=0
{2x+4y=1
{x=-y
{2*(-y)+4y=1
{x=-y
{2y=1/:2
{x=-y
{y=½
{x=-½
{y=½
e) {3x-2y=3
{3x+y=1½
{3x-2y=3
{y=1½-3x
{3x-2*(1½-3x)=3
{y=1½-3x
{3x-5+6x=3
{y=1½-3x
{9x=8/:9
{y=1½-3x
{x=⁸/₉
{y=1½-3*(⁸/₉)
{x=⁸/₉
{y=1½-2⅔
{x=⁸/₉
{y=-⁵/₆
f) {x+2y=-½
{3x+4y=-1
{x=-½-2y
{3*(-½-2y)+4y=-1
{x=-½-2y
{-³/₂-6y+4y=-1
{x=-½-2y
{-2y=½/:(-2)
{x=-½-2y
{y=-¼
{x=-½-2*(-¼)
{y=-¼
{x=0
{y=-¼
