Question

Решить систему уравнений (скрины прикреплены)

Answer 1

Объяснение:

1)

$\left \{\begin{array}{l}9y + x^{2} = 9, \\ x-y = -1 \end{array} \right.\Leftrightarrow \left \{\begin{array}{l}9(x+1) + x^{2} = 9, \\ y =x +1 \end{array} \right.\Leftrightarrow\left \{\begin{array}{l}9x+9 + x^{2} = 9, \\ y =x +1 \end{array} \right.\Leftrightarrow$

$\Leftrightarrow\left \{\begin{array}{l}9x + x^{2} = 0, \\ y =x +1 \end{array} \right.\Leftrightarrow\left \{\begin{array}{l}x(9 + x) = 0, \\ y =x +1 \end{array} \right.\Leftrightarrow \left \{\begin{array}{l} \left [\begin{array}{l} x = 0, \\ 9+x =0\end{array} \right.\\ y =x +1 \end{array} \right.\Leftrightarrow$

$\Leftrightarrow \left \{\begin{array}{l} \left [\begin{array}{l} x = 0, \\ x =-9; \end{array} \right.\\ y =x +1 ;\end{array} \right.\Leftrightarrow \left [\begin{array}{l} \left \{\begin{array}{l} x=0, \\ y = 1 ;\end{array} \right. \\ \left \{\begin{array}{l} x=-9 , \\ y=-8 .\end{array} \right. \end{array} \right.$

ответ : (0; 1) и ( -9; -8)

2) $\left \{\begin{array}{l} x^{2}+y^{2} = 85, \\ y-x = 7 ;\end{array} \right.\Leftrightarrow \left \{\begin{array}{l} x^{2} +(x+7)^{2} = 85, \\ y =x +7; \end{array} \right.\Leftrightarrow\left \{\begin{array}{l} x^{2}+x^{2}+14x+49 = 85, \\ y =x +7; \end{array} \right.\Leftrightarrow$

$\Leftrightarrow\left \{\begin{array}{l} 2x^{2}+14x+49 - 85=0, \\ y =x +7; \end{array} \right.\Leftrightarrow\left \{\begin{array}{l} 2x^{2}+14x - 36=0|:2 , \\ y =x +7; \end{array} \right.\Leftrightarrow$

$\left \{\begin{array}{l} x^{2}+7x - 18=0 , \\ y =x +7.\end{array} \right.$

Решим первое уравнение системы

$x^{2} +7x-18=0;\\D= 7^{2} -4\cdot1\cdot(-18)= 49+72=121=11^{2} ;\\\\x{_1}= \dfrac{-7-11}{2} =\dfrac{-18}{2}=-9 ;\\\\x{_2}= \dfrac{-7+11}{2} =\dfrac{4}{2}=2 .$

Если х= -9, то $y=-9+7=-2$

Если х= 2, то $2+7=9$

Тогда (-9; -2) и ( 2; 9) - решение системы.

ответ : (-9; -2) и ( 2; 9)