Question

Temat : Układy równan

1) 4x + y = 5
-x - 3y = -4

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

3) 1/4x - 1/3y = 1/2
-x - 5 = y

Answer 1

1) 4x + y = 5
-x - 3y = -4 / *4

 

4x + y = 5

-4x - 12y = -16

_________________

4x - 4x + y - 12y = 5 - 16

-11y = -11 /:(-11)

y = 1

 

4x + 1 = 5

4x = 5 - 1

4x = 4 /:4

x = 1

 

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

 

x + 4y = 8

-x + y = 2

________________

x - x + 4y + y = 8 + 2

5y = 10 /:5

y = 2

 

1/2x + 2 * 2 = 4

1/2x + 4 = 4

1/2x = 4 - 4

1/2x = 0 /*2

x = 0

 

3) 1/4x - 1/3y = 1/2 /*12
-x - 5 = y

 

3x - 4y = 6

-x - y = 5 /*3

 

3x - 4y = 6

-3x - 3y = 15

______________

3x - 3x - 4y - 3y = 6 + 15

-7y = 21 /:(-7)

y = -3

 

-x - 5 = -3

-x = - 3 + 5

-x = 2

x = -2

Answer 2

 

 

1)

{4x+y =5

{-x - 3y = -4 |*4

 

{4x+y=5

{-4x-12y=-16

 

{-11y=-11

{y=1

 

{x=1

{y=1

 

2)

{1/2x + 2y=4

{x-y=-2 |*2

 

{1/2x+2y=4

{2x-2y=-4

 

{2,5x=0

{x = 0

 

{x=0

{y=2

 

3

1/4x - 1/3y = 1/2 |*12
-x - 5 = y

 

 

 

3x - 4y = 6

 

-x - y = 5 |*3

 

 

 

3x - 4y = 6

 

-3x - 3y = 15

 

 

 

-7y = 21 |:(-7)

y=-3

 

 

y = -3

 

x = -2