Question

Rozwiąż układ równań
a) -3x+2y= -1
2x-3y= 1
b) 2x+5y= -6
7x+4y= -21
c) 8x+2y= 24
-5x-6y= -18

Answer 1

A)
-3x + 2y = -1    / *2
2x - 3y =  1     / *3

-6x + 4y  = -2
 6x -  9y  =  3
   ------------------
      -5y = 1  / :(-5)
         y = - 1/5

2x - 3y = 1
2x  = 1 + 3y
2x = 1 + 3 * (-1/5) 
2x = 1 - 3/5
2x = 5/5 - 3/5       (5/5 = 1)
2x = 2/5     /:2
x = 2/5 * 1/2
x = 2/10 = 1/5

x = 1/5
y = - 1/5

b)
2x + 5y = -6      / * 7
7x + 4y = -21   / * (-2)

14x + 35y = -42
-14x - 8y = 42
  -----------------
         27y = 0 /:27
            y = 0

2x + 5y = -6
2x = - 6 -5y
2x = - 6 - 5 * (0) 
2x = - 6 /: 2
 x = -3 

x = -3
y = 0

c)
8x + 2y = 24   / * 3
- 5x - 6y = -18

24x + 6y = 72
- 5x - 6y = -18
---------------------
19x        = 54     /: 19

x = 54/19

8x + 2y= 24
2y = 24 - 8x
2y = 24 - 8 *54/19 
2y = 24 - 432/19
2y = 24 - 22 14/19 
2y = 23 19/19 - 22 14/19
2 y = 1 5/19   /:2
y = 24/19 * 1/2
y =  24/38
y =  12/19

x = 54/19
y = 12/19