Question

Rozwiąż układ równań

a) 2x+y-4=3(2x-y)
3(2x-3y)=2x+y-4

b) 2x-(y-2)²=3-(y-1)(y+1)
y- 2×-y/6 =½- 2y-×/4

c) ⅖x-½y=2
³/₄x+2y=6

2×-y/6 - ułamek
2y-×/4 - ułamek

Answer 1

A) 2x+y-4=3(2x-y)
3(2x-3y)=2x+y-4

2x+y-4= 6x - 3y
6x -9y= 2x+y-4

4y= 6x-2x +4 /4
6x -9y= 2x+y-4

y= x+1
6x- 9(x+1)= 2x+ x+1 -4

y=x+1
6x- 9x - 9= 3x-3

y=x+1
6x-9x-3x= -3 +9

y=x+1
-6x= 6

y=x+1
x=1

x=1
y=2

2) 2x-(y-2)²=3-(y-1)(y+1)
y- 2×-y/6 =½- 2y-×/4

2x - y2-4y +4= 3- (y2 -1)
y- 2x - y/6= 1/2 -2y- x/4 /*12

2x-y2-4y+4= 3 - y2+1
12y- 24x- 2y= 6- 24y- 3x

2x-4y=3+1-4
12y- 24x- 2y= 6- 24y- 3x

2x= 4y
12y- 24x- 2y= 6- 24y- 3x

x=2y
12y- 48y- 2y = 6-24y- 6y

x=2y
-8y= 6

x=2y
y= -6/8

x=2y
y=-0,75

x= -3/4 * 2= -3/2
y=-3/4

c) ⅖x-½y=2 / *10
³/₄x+2y=6 /*4

4x-5y=20
3x+8y=24

4x=20+5y
3x+8y=24

x= 20+5y /4
3 (20+5y /4) +8y = 24

x=20+5y/4
60+15y/4 +8y= 24

x=20+5y/4
15+15y +8y=24

x=20+5y/4
23y=9

x=20+5y/4
y=9/23

x= 5+ 54/23
y=9/23