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[tex]a)\\\\\begin{cases}3x+4y=2\\x-3y=5\ \ /\cdot(-3)\end{cases}\\\\\\+\begin{cases}3x+4y=2\\-3x+9y=-15\end{cases}\\----------\\13y=-13\ \ /:13\\y=-1\\\\\\3x+4\cdot(-1)=2\\\\3x-4=2\\\\3x=2+4\\\\3x=6\ \ /:3\\\\x=2\\\\\\\begin{cases}x=2\\y=-1\end{cases}[/tex]

[tex]b)\\\\\begin{cases}2x+5y=3\\4x-10y=2\ \ /:(-2)\end{cases}\\\\\\+\begin{cases}2x+5y=3\\-2x+5y=-1\end{cases}\\----------\\10y=2\ \ /:10\\\\y=\frac{2}{10}=\frac{1}{5}\\\\\\2x+\not5\cdot\frac{1}{\not5}=3\\\\2x+1=3\\\\2x=3-1\\\\2x=2\ \ /:2\\\\x=1\\\\\\\begin{cases}x=1\\y=\frac{1}{5}\end{cases}[/tex]

[tex]c)\\\\\begin{cases}-\frac{1}{2}x+y=4\ \ /\cdot2\\2x-4y=-16\ \ /:2\end{cases}\\\\\\+\begin{cases}-x+2y=8\\x-2y=-8\end{cases}\\---------\\0=0\\\\Uklad\ \ r\'owna\'n\ \ nieoznaczony\ \ ma\ \ niesko\'nczenie\ \ wiele\ \ rozwiaza\'n[/tex]

Basetlago Basetlago · Answer 2

a)

3x + 4y = 2 /·3

x - 3y = 5 /·4

9x + 12y = 6

4x - 12y = 20

------------------- + (dodajemy stronami)

13x = 26 /:13

x = 2

4y = 2 - 3x = 2 - 3 · 2 = 2 - 6 = -4

4y = -4 /:4

y = -1

{x = 2

{y = -1

b)

2x + 5y = 3 /·2

4x - 10y = 2

4x + 10y = 6

4x - 10 y = 2

--------------------- +

8x = 8 /:8

x = 1

5y = 3 - 2x = 3 - 2 · 1 = 3 - 2 = 1

5y = 1 /:5

y = 1/5

{x = 1

{y = 1/5

c)

-1/2 x + y = 4 /·4

2x - 4y = -16

-2x + 4y = 16

2x - 4y = -16

-------------------- +

0 = 0

Układ równań nieoznaczony, nieskończenie wiele rozwiązań.