Решите систему уравнений:x+y=1x^2+y^2=25. Created by БезПОНТОВая. algebra-ru

Решите систему уравнений:x+y=1x^2+y^2=25...

БезПОНТОВая @БезПОНТОВая

July 2022 1 4 Report

Решите систему уравнений:

x+y=1

x^2+y^2=25

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lilyatomach

Verified answer

Ответ:

(4;-3), (-3;4)

Объяснение:

$\left \{ \begin{array}{lcl} {{x+y=1,} \\ {x^{2} +y^{2} =25;}} \end{array} \right.\Leftrightarrow \left \{ \begin{array}{lcl} {{x=1-y,} \\ {(1-y)^{2} +y^{2} =25;\\}} \end{array} \right.\Leftrightarrow \left \{ \begin{array}{lcl} {{x=1-y,} \\ {1-2y+y^{2}+y^{2} -25=0; }} \end{array} \right.$

$\Leftrightarrow\left \{ \begin{array}{lcl} {{x=1-y,} \\ {2y^{2} -2y-24=0;}} \end{array} \Leftrightarrow\right.\left \{ \begin{array}{lcl} {{x=1-y,} \\ {y^{2} -y-12=0;}} \end{array} \right.\Leftrightarrow \left \{ \begin{array}{lcl} {{x=1-y,} \\ {\left [ \begin{array}{lcl} {{y=-3,} \\ {y=4;}} \end{array} \right.} \end{array} \right.$

$\Leftrightarrow \left [ \begin{array}{lcl} {\left \{ \begin{array}{lcl} {{x=4,} \\ {y=-3;}} \end{array} \right.{} \\ {\left \{ \begin{array}{lcl} {{x=-3,} \\ {y=4.}} \end{array} \right.}} \end{array} \right.$

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