Question

Яка з пар чисел є розв’язком системи рівнянь { x2+ у2=10, у-2х=5
А) (3;1) Б) (3;-1) В) (-3;1) Г) (-3;-1)​

Answer 1

Ответ:

Г) (- 3; - 1)

Объяснение:

{ x² + y² = 10

{ y - 2x = 5

{ x² + y² = 10

{ y = 5 + 2

x² + (5 + 2x)² = 10

x = - 3

x = - 1

Answer 2

$\displaystyle\bf\\\left \{ {{x^{2} +y^{2}=10 } \atop {y-2x=5}} \right.\\\\\\\left \{ {{y=2x+5} \atop {x^{2} +(2x+5)^{2} =10}} \right. \\\\\\\left \{ {{y=2x+5} \atop {x^{2} +4x^{2} +20x+25 =10}} \right. \\\\\\\left \{ {{y=2x+5} \atop {5x^{2} +20x+15=0 \ |:5}} \right.\\\\\\\left \{ {{y=2x+5} \atop {x^{2} +4x+3=0}} \right.\\\\\\\left \{ {{y=2x+5} \atop {\left[\begin{array}{ccc}x_{1} =-1\\x_{2} =-3\end{array}\right }} \right. \\\\\\x_{1}=-1 \ \ \Rightarrow \ \ y_{1} =2\cdot(-1)+5=3$

$\displaystyle\bf\\x_{2}=-3 \ \ \Rightarrow \ \ y_{2}=2\cdot(-3)+5= -1\\\\\\Otvet \ : \ (3 \ ; \ -1) \ , \ (-3 \ ; \ -1)$

Ответ :  Г (- 3 ; - 1)