Ответ:

(2; 2)

Пошаговое объяснение:

Решить систему уравнений : [tex]\left \{\begin{array}{l} \dfrac{7x+y}{4}-\dfrac{13x-y}{3} = -4, \\\\ \dfrac{x+6y}{14} -\dfrac{8x-3y}{10} = 0 \end{array} \right.[/tex]

Умножим обе части первого уравнения на12, а обе части второго уравнения на 70.

[tex]\left \{\begin{array}{l} \dfrac{7x+y}{4}-\dfrac{13x-y}{3} = -4|\cdot 12, \\\\ \dfrac{x+6y}{14} -\dfrac{8x-3y}{10} = 0|\cdot 70 \end{array} \right.\Leftrightarrow\left \{\begin{array}{l} 3\cdot(7x+y)-4\cdot(13x-y) = -48, \\\\ 5\cdot(x+6y) -7\cdot (8x-3y) = 0 \end{array} \right.\Leftrightarrow[/tex]

[tex]\Leftrightarrow\left \{\begin{array}{l} 21x+3y-52x+4y = -48, \\\\ 5x+30y -56x+21y = 0 \end{array} \right.\Leftrightarrow\left \{\begin{array}{l} -31x+7y = -48, \\\\ -51x+51y = 0 \end{array} \right.\Leftrightarrow[/tex]

[tex]\Leftrightarrow\left \{\begin{array}{l} -31x+7y = -48, \\\\ x-y = 0 \end{array} \right.\Leftrightarrow\left \{\begin{array}{l} -31x+7x = -48, \\\\ y=x \end{array} \right.\Leftrightarrow\left \{\begin{array}{l} -24x = -48, \\\\ y=x \end{array} \right.\Leftrightarrow[/tex]

[tex]\Leftrightarrow\left \{\begin{array}{l} x = -48:(-24) , \\\\ y=x \end{array} \right.\Leftrightarrow\left \{\begin{array}{l} x = 2 , \\\\ y =2 \end{array} \right.[/tex]

Тогда (2; 2) - решение системы.

Выполним проверку.

[tex]\left \{\begin{array}{l} \dfrac{7\cdot2+2}{4}-\dfrac{13\cdot2-2}{3} = -4, \\\\ \dfrac{2+6\cdot2}{14} -\dfrac{8\cdot2-3\cdot 2}{10} = 0; \end{array} \right.[/tex]

[tex]\left \{\begin{array}{l} \dfrac{16}{4}-\dfrac{24}{3} = -4, \\\\ \dfrac{14}{14} -\dfrac{10}{10} = 0; \end{array} \right.[/tex]

[tex]\left \{\begin{array}{l} 4-8=-4 , \\\\ 1-1=0; \end{array} \right.\\\\\left \{\begin{array}{l} -4 = -4 , \\\\ 0 =0. \end{array} \right.[/tex]

Равенства верны.

#SPJ1