Question

Rozwiąż równania dowolną metodą.

d)
(x+1)/3 - (y + 2)/4 = 2(x - y)/5
(x-3)/4 - (y - 3)/3 = 2y - x

h)
11/20 y - 0,8 (1/4 x + 2,5) = 2, 1/2
(6x - 0,3y)/2 - 1, 1/2 = 2(1 + x)

i)
y/2 + x/4 - 1/5 (x + 2) = 1,1
x - 2y + 4 = x/2 + 3/4 (y - 0,5)

Answer 1

I)
y/2 + x/4 - 1/5(x+2)=1,1 / *20
x-2y+4=x/2 + 3/4(y-0,5) / *4

10y + 5x - 4(x+2)=22
4x-8y+16=2x+3(y-0,5)

10y+5x-4x-8=22
4x-8y+16=2x+3y-1,5

x=30-10y
2x-11y=-17,5

x=30-10y
60-20y-11y=-17,5

x=30-10y
-31y=-77,5

x=30-10y
y=2,5

x=30-25
y=2,5

x=5
y=2,5

Answer 2

D)
(x+1)/3 - (y + 2)/4 = 2(x - y)/5 /*60
(x-3)/4 - (y - 3)/3 = 2y - x /*12

20x+20-15y-30=30x-30y
3x-9-4y+12=24y-12x

20x-30x-15y+30y=30-20
3x+12x-4y-24y=-12+9

-10x+15y=10 /*3
15x-28y=-3 /*2

-30x+45y=30
30x-56y=-6

-11y=24
y=-11/24

-10x+15*(-11/24)=10
-10x-6 7/8=10
-10x=10+6 7/8
-10x=135/8
x=-1 11/14

x=-1 11/14
y=-11/24

h)
11/20 y - 0,8 (1/4 x + 2,5) = 2, 1/2 /*10
(6x - 0,3y)/2 - 1, 1/2 = 2(1 + x) /*10

22y-8(1/4x+2,5)=25
30x-1,5y-15=20(1+x)

22y-2x-20=25
30x-1,5y-15=20+20x

22y-2x=45 /*5
-1,5y+10x=35

110y-10x=225
-1,5y+10x=35

108,5y=260
y=2 43/260

22*563/260-2x=45
47 166/260-2x=45
-2x=-2 166/260
x=686/260*(-1/2)
x=1 166/260

x=1 166/260
y=2 43/260

i)
y/2 + x/4 - 1/5 (x + 2) = 1,1 /*10
x - 2y + 4 = x/2 + 3/4 (y - 0,5) /*4

5y+2,5x-2x-4=11 /*10
4x-8y+16=2x+3y-1,5 /*10

50y+25-20x-40=110
40x-80y+160=20x+30y-15

-20x+50y=125
20x-50y=-175

0=50