Question

Rozwiąż układ metodą przeciwnych wspołczynników

a)
2x-3y=4
x-y=1


b)
¾x-⅔y=¹₁₂(jedna dwunasta)
6x+4y=4

Answer 1

A)
2x - 3y = 4
x - y = 1/* (-3)

2x - 3y = 4
-3x + 3y = -3
...............dodajemy stronami
-x = 1
x = -1

x - y = 1
- y = 1 - x / *(-1)
y = x - 1
y = -2


b)
¾x-⅔y = 1/12 / * 12
6x+4y=4 /* 2

9x - 8y = 1
12x + 8y = 8
..............dodajemy stronami
21x = 9 /: 21
x = 9/21
x = 3/7

6x+4y=4
6 * 3/7 + 4y = 4
4y = 4 - 18/7
4y = 28/7 - 18/7
4y = 10/7 :4
y = 5/14

Answer 2

A)
2x-3y=4
x-y =1 /* (-2)

2x-3y=4
-2x+2y=-2
-------------
-y=2
y=-2


2x-3y=4
x-y =1 /*(-3)

2x-3y=4
-3x+3y=-3
-------------
-x=1
x=-1

x=-1
y=-2

b)
¾x-⅔y=¹/₁₂ /*12
6x+4y=4 /*2

9x-8y=1
12x+8y=8
-----------------
21x=9 /:21
x=9/21
x=3/7

9x-8y=1 /*(-4)
12x+8y=8 /*3

-36x+32y=-4
36x+24y=24
-----------------
56y=20 /:56
y=20/56
y=5/14

x=3/7
y=5/14