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

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

Ответ: $(5;0)$