Ответ:

а) (2;2) б) (3;2) в) [tex]\frac{9}{58} ;-\frac{5}{58}[/tex] г) [tex]\frac{37}{45} ; \frac{5}{9}[/tex]

Объяснение:

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Решение.

Метод сложения решения систем линейных уравнений .

[tex]1.\ \left\{\begin{array}{l}\bf 3x+5y=16\ |\cdot (-2)\\\bf 6x-2y=8\end{array}\right\ +\ \left\{\begin{array}{l}\bf -12y=-24\\\bf 6x=2y+8\ |:2\end{array}\right\ \ \left\{\begin{array}{l}\bf y=2\\\bf 3x=y+4\end{array}\right\\\\\\\left\{\begin{array}{l}\bf y=2\\\bf 3x=6\end{array}\right\ \ \left\{\begin{array}{l}\bf y=2\\\bf x=2\end{array}\right[/tex]

Ответ:  (2;2) .

[tex]\bf 2.\ \left\{\begin{array}{l}\bf 2x-5y=-4\ |\cdot 2\\\bf 7x+10y=41\end{array}\right\ +\ \left\{\begin{array}{l}\bf 11x=33\\\bf 5y=2x+4\end{array}\right\ \ \left\{\begin{array}{l}\bf x=3\\\bf 5y=10\end{array}\right\ \ \left\{\begin{array}{l}\bf x=3\\\bf y=2\end{array}\right[/tex]

Ответ:  (3;2) .

[tex]3.\left\{\begin{array}{l}\bf 9x-7y=2\ |\cdot 2\\\bf 2x-8y=1\ |\cdot (-9)\end{array}\right\ +\ \left\{\begin{array}{l}\bf 58y=-5\\\bf 2x=8y+1\end{array}\right\ \ \left\{\begin{array}{l}\bf y=-\dfrac{5}{58}\\\bf 2x=-\dfrac{40}{58}+1\end{array}\right\\\\\\\left\{\begin{array}{l}\bf y=-\dfrac{5}{58}\\\bf 2x=\dfrac{18}{58} \end{array}\right\ \ \left\{\begin{array}{l}\bf y=-\dfrac{5}{58}\\\bf x=\dfrac{9}{58} \end{array}\right[/tex]  

Ответ:  [tex]\bf \Big(\ \dfrac{9}{58}\ ;-\dfrac{5}{58}\ \Big)[/tex]  .

[tex]4.\ \left\{\begin{array}{l}\bf 5x-2y=3\ \ \ \ |\ \cdot 5\\\bf 10x+5y=11\ |\cdot 2\end{array}\right\ +\ \left\{\begin{array}{l}\bf 45x=37\\\bf 5y=11-10x\end{array}\right\ \ \left\{\begin{array}{l}\bf x=\dfrac{37}{45}\\\bf 5y=11-\dfrac{370}{45}\end{array}\right[/tex]

[tex]\left\{\begin{array}{l}\bf x=\dfrac{37}{43}\\\bf \ 5y=\dfrac{125}{45}\end{array}\right\ \ \left\{\begin{array}{l}\bf x=\dfrac{37}{45}\\\bf \ \ y=\dfrac{25}{45}\end{array}\right\ \ \left\{\begin{array}{l}\bf \ x=\dfrac{37}{45}\\\bf y=\dfrac{5}{9}\end{array}\right[/tex]  

Ответ:  [tex]\bf \Big(\ \dfrac{37}{45}\ ;\ \dfrac{5}{9}\ \Big)\ .[/tex]