Question

Решить систему уравнений x-y=5 X^2-y^2=25

Answer 1

X = y + 5
(y + 5)² - y² = 25

x = y + 5
y² + 10y + 25 - y² = 25

x = y + 5
10y = 0

y = 0
x = 0 + 5

x = 5
y = 0
Ответ: (5; 0).

Answer 2

$\left[\begin{array}{ccc}x-y=5\\x^2-y^2=25\end{array}\right\left[\begin{array}{ccc}y=x-5\\x^2-y^2=25\end{array}\right\\\\x^2-(x-5)^2=25\\x^2-(x^2-10x+25)=25\\x^2-x^2+10x-25=25\\10x=50\\x=5\\y=5-5=0$

Ответ: $(5;0)$