Question

Oblicz układy równań !! :

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

b) x/5-y/4=4
3x+4y=-2

c) 2x/3+4y/5=-2
x/2-y/10=2

d) 2x-3y=-5
-x+5y=6

Answer 1

A) 4y=3x-4 
2x=-3(y+5)-1

4y=  3x-4  |:4
2x = -3y - 15 -1

y = (3x-4)/4
2x= - 3*(3x-4)/4 - 16  |*4

y = (3x-4)/4
8x=-9x+12-64

y = (3x-4)/4
17x = -52  |:17

y = (3x-4)/4
x = -52/17 = -3 1/17

y = (3*(-52/17)-4)/4
x = -3 1/17

y = (-156/17 - 68/17)/4 = (-224/17)/4 = -224/68 = - 3 20/68 = -3 5/17
x = - 3 1/17


b) x/5-y/4=4    |*5
3x+4y=-2 

x - 5y/4 = 20
3x+4y = -2   

Answer 2

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

4y=  3x-4  |:4
2x = -3y - 15 -1

y = (3x-4)/4
2x= - 3*(3x-4)/4 - 16  |*4

y = (3x-4)/4
8x=-9x+12-64

y = (3x-4)/4
17x = -52  |:17

y = (3x-4)/4
x = -52/17 = -3 1/17

y = (3*(-52/17)-4)/4
x = -3 1/17

y = (-156/17 - 68/17)/4 = (-224/17)/4 = -224/68 = - 3 20/68 = -3 5/17
x = - 3 1/17


b) x/5-y/4=4    |*5
3x+4y=-2

x - 5y/4 = 20
3x+4y = -2  

x = 20+5/4y
3(20+5/4y) + 4y = -2

x = 20+5/4y
60 + 15/4y + 4y = -2

x = 20+5/4y
15/4y + 16/4y = -2-60

x = 20+5/4y
31/4y = -62  |*4/31

x = 20+5/4y
y = -62 * 4/31 = -2*4 = -8

x = 20+5/4*(-8)
y =-8

x = 20 - 10
y = -8

x = 10
y = -8


c) 2x/3+4y/5=-2  |*15
x/2-y/10=2    |*10

10x+12y= -30
5x-y=20  |*(-2)

10x+12y = -30
-10x+2y = -40
+-----------------------
14y = -70    |:14
y = -5
5x-(-5) = 20
5x+5 = 20
5x = 15  |:5
x = 3
y = -5


d) 2x-3y = -5
-x +5y = 6  |*2

2x - 3y = -5
-2x + 10y = 12
+----------------------------
7y = 7  |:7
y = 1
-x + 5*1 = 6
-x = 1  |*(-1)
x = -1
y = 1