Question

Rozwiąż układy równań

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Answer 1

Verified answer

a)

[tex]\left\{\begin{array}{l}-2x+5y=19 |\cdot 7\\7x-8y=-38|\cdot 2\end{array}\right.\\\\\underline{+\left\{\begin{array}{l}-14x+35y=133\\14x-16y=-76\end{array}\right.}\\\\-14x+14x+35y-16y=133-76\\19y=57 |:19\\\underline{y=3}\\\\-2x+15=19 |-15\\-2x=4 |:(-2)\\\underline{x=-2}\\\\\boxed{\left\{\begin{array}{l}x=-2\\y=3\end{array}\right.}[/tex]

b)

[tex]\left\{\begin{array}{l}-8x+9y=79|\cdot 2\\-5x-2y=-4|\cdot 9\end{array}\right.\\\\\underline{+\left\{\begin{array}{l}-16x+18y=158\\-45x-18y=-36\end{array}\right.}\\\\-16x-45x+18y-18y=158-36\\-61x=122 |:(-61)\\\underline{x=-2}\\\\10-2y=-4 |-10\\-2y=-14 |:(-2)\\\underline{y=7}\\\\\boxed{\left\{\begin{array}{l}x=-2\\y=7\end{array}\right.}[/tex]

Answer 2

Odpowiedź:

1.

- 2 x + 5 y = 19  / * 7

7 x -  8 y = - 38  / * 2

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

- 14 x + 35 y = 133

14 x -   16 y  = - 76

-------------  dodajemy stronami

19 y = 57  / : 19

y = 3

------

- 2 x + 5*3 = 19

-2 x = 19 - 15

-2 x = 4  /:  ( - 2)

x =  - 2

Odp.    x = - 2 ,   y = 3

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2.

- 8 x + 9 y = 79 /  * 2

- 5 x -2 y = - 4   / * 9

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

- 16 x + 18 y = 158

- 45 x  - 18 y = - 36

-------------  dodajemy stronami

- 61 x = 122  / :  ( - 61 )

x = - 2

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

- 8* ( -2)  + 9 y = 79

16 + 9 y = 79

9 y = 79 - 16

9 y = 63  / :   9

y =  7

Odp.   x = - 2 ,  y = 7

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