3(x-2y)\5 + (5x - 3y)\3 = x +1 /*15
(2x - 3y)\3 - (4x - 3y)\2 = y - 5 /*6
9(x-2y) + 5(5x - 3y) = 15x +15
2(2x - 3y) - 3(4x - 3y) = 6y - 30
9x-18y + 25x - 15y = 15x +15
4x - 6y - 12x + 9y = 6y - 30
9x-18y + 25x - 15y -15x= 15
4x - 6y - 12x + 9y -6y = - 30
19x+33y=15
-8x=-30+3y /*(-1)
19x+33y=15
8x=30-3y
19x+33y=15
-8x-3y=-30
19x+33y=15
-3y=-30+8x /*(-1)
19x+33y=15
3y=30-8x
19x+33y=15
y=10-8/3x
19x+33(10-8/3x)=15
y=10+8/3x
19x+330-88x=15
y=10-8/3x
-69x=15-330
y=10-8/3x
-69x=- 315 /*(-1)
y=10-8/3x
69x= 315
y=10-8/3x
x= 315/69
y=10-8/3*315/69
x= 315/69
y=510/23
x= 4 39/69
y=22 4/23
-------------------------
b)
-4x +3y = 1
3x + 4y = 18
3y=1+4x
3x + 4y = 18
y=⅓+4/3x
3x + 4(⅓+4/3x) = 18
y=⅓+4/3x
3x + 4/3+16/3x = 18
y=⅓+4/3x
25/3x = 18- 4/3
y=⅓+4/3x
25/3x = 50/3
y=⅓+4/3x
x = 50/3*3/25
y=⅓+4/3x
x=2
y=⅓+4/3*2
x=2
y=3
x=2
-------------------------
( x - 2) ( x + 2) + 2y = ( x - 2)² + y
3x + 2y = 11
x²-4+2y=x²-4x+4+y
3x + 2y = 11
x²-x²+4x=4+y+4-2y
3x + 2y = 11
y=8-4x
3x + 2y = 11
y=8-4x
3x + 2(8-4x) = 11
y=8-4x
3x+16-8x=11
y=8-4x
-5x=11-16
y=8-4x
-5x=-5
y=8-4x
x=1
y=4
x=1
--------------------------
d)
4x - 6y = 0
3x + y = x + 11
4x=6y
3x -x= 11-y
x=1,5y
2x=11-y
x=1,5y
2*1,5y=11-y
x=1,5y
3y+y=11
x=1,5y
4y=11
x=1,5y
y=11/4
x=1,5*11/4
y=11/4
x=33/8
y=11/4
x=4 1/8
y=2 3/4
---------------------
e)
(x -2)² - 2(x - 2) = 1 - (3 -x) (3 + x)
2x + y = 4
x²-4x+4-2x+4=1-9+x²
y=4-2x
x²-6x-x²=-8-8
y=4-2x
-6x=-16 /*(-1)
y=4-2x
6x=16
y=4-2x
x=8/3
y=4-2*8/3
x=8/3
y=-4/3
------------------
(x + 1)² + y² - 8 = (y - 2)² +( x - 3) ( x + 3)
3x - y +4 = 0
x²+2x+1+y²-8=y²-4y+4+x²-9
y=3x+4
2x+4y=2
y=3x+4
2x+4(3x+4)=2
y=3x+4
2x+12x+16=2
y=3x+4
14x=-14
y=3x+4
x=-1
y=-3+4
x=-1
y=1
----------------------------
2x - y = 5
4x - 2y= 3
-y=-2x+5 /*(-1)
4x - 2y= 3
y=2x-5
4x - 2(2x-5)= 3
y=2x-5
4x - 4x+10= 3
y=2x-5
10≠ 3 ukł. równań sprzecznych
--------------------------
-x + 2y = 3
3x - 6y = -9
-x=-2y+3 /*(-1)
3x - 6y = -9
x=2y-3
3(2y-3) - 6y = -9
x=2y-3
6y-9 - 6y = -9
x=2y-3
-9 = -9 układ nieoznaczony posiada wiele rozwiazań
