Question

Rozwiąż układ równań dowolną metodą

a)

{-1/2x - 1/4y=1

{-5x + y=3

b)

{(x-1)/2 +(y+1)=3

{(x+1)/3 - (y-2)/6=2

c)

{(x-y)/2 - (x+y)/4=1

{(2x+y)/3 - (x+y)/2=0

Answer 1

a) 

{-1/2x  - 1/4y=1

{-5x + y=3

 

 

{-1/2x - 1/4y = 1

{ y = 3+5x

 

{-1/2x - 1/4 * (3+5x) = 1

{ y= 3 + 5x

 

{-1/2x - 3/4 - 5x = 1

{y = 3 +5x

 

{ -5 1/2x = 1 + 3/4 /:(-5 1/2)

{y=3+5x

 

{x = 7/4 * (-2/11)

{y = 3+5x

 

{x= -7/22

{y = 3+ 5/1 * (-7/22)

 

{x = -7/22

{y = 3 + 35/22

 

{x= -7/22
{y = 4 13/22

 

b)  

{(x-1)/2 +(y+1)=3

{(x+1)/3 - (y-2)/6=2

 

{(x-1)/2 +(y+1)=3/*2

{(x+1)/3 - (y-2)/6=2/*6

 

{x+1+2y+2=6

{2x+2-y-2=12

 

{x+2y+3=6

{2x-y=12

 

{ x = 3-2y

{ 2(3-2y)-y=12

 

{x = 3-2y

{6 - 4y - y =12

 

{x = 3 - 2y

{-5y = 12-6  /:(-5)

 

{x = 3-2y

{y = 6 * (-1/5)

 

{x = 3-2 *1 1/5

(y = 1 1/5

 

{x= 3 - 2 2/5

{y = 1 1/5

 

{x = 3/5

{y = 1 1/5

 

c) 

{(x-y)/2 - (x+y)/4=1

{(2x+y)/3 - (x+y)/2=0

 

{(x-y)/2 - (x+y)/4=1 /*4

{(2x+y)/3 - (x+y)/2=0 /*6

 

{2x - 2y - x +y = 4

{4x + 2y -3x + 3y = 0

 

{x-y=4

{x+5y=0

 

{x=4+y

{4+y+5y=0

 

{x=4+y

{6y = -4 /:6

 

{x = 4+y

{y = - 2/3

 

{x= 4 + (-2/3)

{y = -2/3

 

{x = 3/13
{y= -2/3