Вправа 583 алгебра Істер гдз 9 клас

Задача №583
Умова:
Знайдіть розв'язки системи рівнянь:
1. $$
\left\{\begin{array}{l}
x-y=2 \\
x^2+y^2=34
\end{array}\right.
$$ 2. $$
\left\{\begin{array}{l}
x+y=9 \\
x^2-y^2=9
\end{array}\right.
$$
$$
\begin{aligned}
& \left\{\begin{array}{l}
x-y=2, \\
x^2+y^2=34 .
\end{array}\right. \\
& \left\{\begin{array}{l}
x=y+2, \\
(y+2)^2+y^2=34 .
\end{array}\right. \\
& \left\{\begin{array}{l}
x=y+2, \\
y^2+4 y+4+y^2=34 .
\end{array}\right. \\
& \left\{\begin{array}{l}
x=y+2, \\
2 y^2+4 y-30=0 .
\end{array}\right. \\
& \left\{\begin{array}{l}
x=y+2, \\
y^2+2 y-15=0 .
\end{array}\right. \\
& \left\{\begin{array}{l}
x=y+2, \\
(y-3)(y+5)=0 .
\end{array}\right. \\
& \left\{\begin{array}{l}
y=3, \quad x=3+2=5 \\
y=-5, \quad x=-5+2=-3 .
\end{array}\right.
\end{aligned}
$$
Відповідь: $$
\begin{aligned}
& (5,3) \text { або }(-3,-5) \text {. } \\
& \left\{\begin{array}{l}
x+y=9, \\
x^2-y^2=9 .
\end{array}\right. \\
& \left\{\begin{array}{l}
x+y=9 \\
(x-y)(x+y)=9 .
\end{array}\right. \\
& \left\{\begin{array}{l}
x+y=9 \\
(x-y)(9)=9 .
\end{array}\right. \\
& \left\{\begin{array}{l}
x+y=9 \\
x-y=1
\end{array}\right. \\
& \left\{\begin{array}{l}
x=\frac{9+1}{2}=5, \\
y=\frac{9-1}{2}=4 .
\end{array}\right.
\end{aligned}
$$
Відповідь: $$
(5,4)
$$