Odpowiedź :
Odpowiedź:
a)
x + 4y + 2 = 2x + 3y + 6
3 - x + 2y = 1 - 3x - 2y
x - 2x + 4y - 3y = 6 - 2
- x + 3x + 2y + 2y = 1 - 3
- x + y = 4 | * 2
2x + 4y = - 2
- 2x + 2y = 8
2x + 4y = - 2
dodajemy rownania
- 2x + 2x + 2y + 4y = 8 - 2
6y = 6
y = 6/6 = 1
- x + y = 4
- x + 1 = 4
- x = 4 - 1 = 3
x = - 3
Odp: x = - 3 , y = 1
b)
- x + y + 7 = 2x + 3y + 9
2x + y + 10 = - 4x + 3y + 30
- x - 2x + y - 3y = 9 - 7
2x + 4x + y - 3y = 30 - 10
- 3x - 2y = 2
6x - 2y = 20
odejmujemy równania
- 3x - 6x - 2y + 2y = 2 - 20
- 9x = - 18
9x = 18
x = 18/9 = 2
- 3x - 2y = 2
- 3 * 2 - 2y = 2
- 6 - 2y = 2
- 2y = 2 + 6 = 8
2y = - 8
y = - 8/2 = - 4
Odp: x = 2 , y = - 4
c)
3x - 4y + 6 = x - 3y + 7
4 - x - y = 2x - 2y + 1
3x - x - 4y + 3y = 7 - 6
- x - 2x - y + 2y = 1 - 4
2x - y = 1
- 3x + y = - 3
dodajemy równania
2x - 3x - y + y = 1 - 3
- x = - 2
x = 2
2x - y = 1
2 * 2 - y = 1
4 - y = 1
- y = 1 - 4
- y = - 3
y = 3
Odp: x = 2 , y = 3
Odpowiedź:
a.
[tex]\left \{ {{x+4y+2=2x+3y+6} \atop {3-x+2y=1-3x-2y}} \right.[/tex]
[tex]\left \{ {{x-2x+4y-3y=6-2} \atop {-+3x+2y+2y=1-3}} \right.[/tex]
[tex]\left \{ {{-x+y=4/*2} \atop {2x+4y=-2}} \right.[/tex]
[tex]\left \{ {{-2x+2y=8} \atop {2x+4y=-2}} \right.[/tex]
-------------------
6y=6/:6
y=1
-x+1=4
-x=4-1
x=3/:(-1)
x=-3
(x,y)=(-3,1)
b.
{-x +y +7 = 2x +3y +9
{2x+y +10 = -4x +3y +30
[tex]\left \{ {{-x-2x+y-3y=9-7} \atop {2x+4x+y-3y=30-10}} \right.[/tex]
[tex]\left \{ {{-3x-2y=2/*(-1)} \atop {6x-2y=20}} \right.[/tex]
[tex]\left \{ {{3x+2y=-2} \atop {6x-2y=20}} \right.[/tex]
------------------
9x=18/:9
x=2
-3*2-2y=2
-6-2y=2
-2y=2+6
-2y=8/:(-2)
y=-4
(x,y)=(2,-4)
c.
{3x -4y +6 =x-3y +7
{4-x -y = 2x -2y +1
[tex]\left \{ {{3x-x-4y+3y=7-6} \atop {-x-2x-y+2y=1-4}} \right.[/tex]
[tex]\left \{ {{2x-y=1} \atop {-3x+y=-3}} \right.[/tex]
------------------
-x=-2/:(-1)
x=2
2*2-y=1
4-y=1
-y=1-4
-y=-3/:(-1)
y=3
(x,y)=(2,3)
Szczegółowe wyjaśnienie: