Question

Rozwiąż układ równań.

a) {2x-3y=10

{3x+5y=0

b)

{3x+y=9

{2x-5y= -11

c)

{3x+2y=13

{2x+y=1

Answer 1

a)

{2x-3y=10    /*5

{3x+5y=0      /*3

 

10x - 15y = 50

9x + 15y = 0

---------------------

19x = 50

x = 50/19

 

2 * 50/19 - 3y = 10

100/19 - 3y = 10

-3y = 10 - 100/19

-3y = 190/19 - 100/19

-3y = 90/19

y = 90/19 * (-1/3)

y = - 30/19

 

x = 50/19

y = -30/19

 

 

 

b)

{3x+y=9      /*5

{2x-5y= -11

 

15x + 5y = 45

2x - 5y = -11

--------------------

17x = 34

x = 2

 

3x + y = 9

y = 9 - 3*2

y = 9 - 6

y = 3

 

x = 2

y = 3

 

c)

{3x+2y=13

{2x+y=1      /*(-2)

 

3x + 2y = 13

-4x - 2y = -2

-----------------

-x = 11

x = -11

 

2x + y = 1

2 * (-11) + y = 1

-22 + y = 1

y = 1 + 22

y = 23

 

x = -11

y = 23