Алгебра 9 класс учебник Макарычев, Миндюк ответы – номер 497

(3x – 1)( – x + 1) = 0
3x – 1 = 0
3x = 1
x₁ = 1/3

или
–x + 1 = 0
–x = –1
x₂ = 1
y₁ = 2 · 1/3 – 1 = –1/3
y₂ = 2 · 1 – 1 = 1

Ответ: (1/3; –1/3), (1; 1)

x – 7y = 0  или  х + 7у = 0
x = 7y                 х = –7у

49y² + y² = 100
50y² = 100
y² = 2
y₁ = $$\sqrt{2}$$, y₂ = –$$\sqrt{2}$$
x₁ = 7 · $$\sqrt{2}$$ = 7$$\sqrt{2}$$
x₂ = 7 · (–$$\sqrt{2}$$) = –7$$\sqrt{2}$$

49y² + y² = 100
50y² = 100
y² = 2
y₁ = $$\sqrt{2}$$, y₂ = –$$\sqrt{2}$$
x₁ = –7 · $$\sqrt{2}$$ = –7$$\sqrt{2}$$
x₂ = –7 · (–$$\sqrt{2}$$) = 7$$\sqrt{2}$$

Ответ: (–7$$\sqrt{2}$$; $$\sqrt{2}$$), (7$$\sqrt{2}$$; –$$\sqrt{2}$$), (7$$\sqrt{2}$$; $$\sqrt{2}$$), (–7$$\sqrt{2}$$; –$$\sqrt{2}$$)

(x – 3)(y – 5) = 0
x – 3 = 0      или       у – 5 = 0
x = 3                          у = 5
3² + y² = 25              x² + 5² = 25
y² = 16                      x² = 0
y₁ = 4, y₂ = –4          х = 0

Ответ: (3; 4), (3; –4), (0; 5)

x(y + 1) = 0
x = 0        или        у + 1 = 0
0² – y² = 50           у = –1
–y² = 50                 x² – (–1)² = 50
Корней нет           x² = 51
                                х₁ = $$\sqrt{51}$$
                                х₂ = –$$\sqrt{51}$$

Ответ: ($$\sqrt{51}$$; –1), (–$$\sqrt{51}$$; –1)