2b

|

21x - 32 = 5x - 8y

||

   5x - 6y = y - 9x

|

  21x - 32 = 5x -8y  |-5x
   16x - 32 = - 8y  |/(-8)
  "" -2x + 4 = y ""

| in ||

  5x-6*(-2x+4) = (-2x+4)-9x
  5x+12x-24 = -2x+4-9x
  17x-24 = 4-11x   |+11x
  28x-24 = 4       |+24
  28x = 28         |/28
  "" x = 1 ""

x = 1 in |

  -2*1+4 = y
  -2+4 = y
  2 = y

prüfe

  5*1-6*2 = 2-9*1
  5-12 = 2-9
  -7 = -7

3a |

4x+2y = 2     |/2
2x+y = 1      |-2x
y = 1-2x 

||

-9x+3y = 33    |+9x
 3y = 33+9x     |/3
 y = 11+3x

| = ||

  1-2x = 11+3x   |+2x
  1 = 11+ 5x     |-11
  -10 = 5x       |/5
  "" -2 = x ""

x=-2 in |

  y = 1-2*(-2)
  y = 1+4
  "" y = 5 ""

prüfe

   5 = 11+3*(-2)
   5 = 5

3b

|

35x-(10y-87) = 10-(32y+20x)
35x-10y+87 = 10-32y-20x   |+10y
35x+87 = 10-22y-20x       |+20x
55x+87 = 10-22y           |-10
55x+77 = -22y             |/(-22)
(-55/22)x+(77/-22) = y
"" -2,5x-3,5 = y ""

||

24x-(16y-15) = 10y-(15x-2)
24x-16y+15 = 10y-15x+2   |+15x
39x-16y+15 = 10y+2       |+16y
39x+15 = 26y+2           |-2
39x+13 = 26y             |/26
"" 1,5x+0,5 = y ""

|=||

-2,5x-3,5 = 1,5x+0,5   |+3,5
-2,5x = 1,5x+4         |-1,5x
-4x = 4                |/(-4)
"" x = -1 ""

x=(-1) in ||

1,5*(-1)+0,5 = y
-1,5+0,5 = y
"" -1 = y ""

prüfe

1,5*(-1)+0,5 = -1
-1,5+0,5 = -1
-1 = -1

4a

|

5x-y = 14

||

-5x-16 = -6y   |+6y
-5x-16+6y = 0      |+16
-5x+6y = 16

|+||

5x-y = 14
-5x+6y = 16
------------
5y = 30   |/5
"" y = 6 ""

y=6 in |

5x-6 = 14   |+6
5x = 20     |/5
"" x = 4 ""

prüfe

5*4-6 = 14
20-6 = 14
14 = 14

4b

|

(x+3)²-2y-x² = 2x+y+16
x²+6x+9-2y-x² = 2x+y+16   |-2x
4x+9-2y = y+16            |+2y
4x+9 = 3y+16              |-16
4x-7 = 3y

||

4(x-y)-(3x-5y) = 7
4x-4y-3x+5y = 7
x+y = 7   |-y |-7
x-7 = -y  |*3
3x-21 = -3y

|+||

4x-7 = 3y
3x-21 = -3y
---------
7x-28 = 0   |+28
7x = 28     |/7
"" x = 4 ""

x=4 in ||

4*4-7 = 3y
16-7 = 3y
9 = 3y   |/3
"" 3 = y ""

prüfe

4*4-7 = 3*3
16-7 = 9
9 = 9