Question

Rozwiąż równania dowolną metodą.
b)
(2x - 1)/5 + (3y - 2)/4 = 2
(3x + 1)/5 - (3y + 2)/4 = 0
c)
(3x - 2y)/5 + (5x - 3y)/3 = x +1
(2x - 3y)/3 + (4x - 3y)/2 = y +1
d)
(x+1)/3 - (y + 2)/4 = 2(x - y)/5
(x-3)/4 - (y - 3)/3 = 2y - x
e)
10(y + 2) + 3(x - 5) = x - 5
25(y + 2) = 3(x - 5) = - 10
f)
2(2x - y) + 3(x + 3y) = 42
5(x + 3y) - 8(2x - y) = - 32
g)
(x + 2y)/4 - ( x - 1/3 y) = 1 + y
(y + 3)/6 + (2 - x)/8 = 3/2
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

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

8x-4+15y-10=40
12x+4-15y-10=0

8x+15y=54
12x-15y=6

20x=60 /:20
x=3


12x-15y=6
12*3 -15y=6
-15y=6-36
-15y=-30 /:(-15)
y=2



c)
(3x - 2y)/5 + (5x - 3y)/3 = x +1 /*15
(2x - 3y)/3 + (4x - 3y)/2 = y +1 /*6

9x-6y+25x-15y=15x+15
4x-6y+12x-9y=6y+6

19x -21y=15
16x-21y=6 /*(-1)

19x-21y=15
-16x+21y=-6

3x=9 /:3
x=3




16x-21y=6
16*3 -21y=6
-21y=6-48
-21y= -42 /:(-21)
y= 2



e)
10(y + 2) + 3(x - 5) = x - 5
25(y + 2) = 3(x - 5) = - 10 tu chyba ma byc + a nie =

10y+20+3x-15=x-5
25y+50+3x-15=-10

10y+2x=-10 /*3
25y+3x=-45 /*(-2)

30y+6x=-30
-50y-6x=90

-20y=60 /:(-20)
y=-3



10y+2x=-10
10*(-3)+2x=-10
2x=-10+30
2x=20 /:2
x=10


f)
2(2x - y) + 3(x + 3y) = 42
5(x + 3y) - 8(2x - y) = - 32

4x-2y+3x+9y=42
5x+15y-16x+8y=-32

7x+7y=42 /:7
-11x+23y=-32

x+y=6
-11x+23y=-32

x=6-y

-11(6-y) +23y=-32
-66+11y+23y=-32
34y=-32+66
34y=34 /:34
y=1


x=6-y
x=6-1
x=5


g)
(x + 2y)/4 - ( x - 1/3 y) = 1 + y /*12
(y + 3)/6 + (2 - x)/8 = 3/2 /*24

3x+6y- 12x +4y=12+12y
4y+12+6-3x=36

-9x-2y=12 /*2
4y-3x=18

-18x-4y=24
-3x+4y=18

-21x=42 /:(-21)
x=-2

4y-3x=18
4y-3*(-2)=18
4y=18-6
4y=12
y=3