§8. Неравенства с двумя переменными и их системы — 25. Некоторые приёмы решения систем уравнений второй степени — 480 — стр. 143

$\{\begin{array}{l}4x(x+y)+y^2=49\\ 4x(x-y)+y^2=81\end{array}$

$\{\begin{array}{l}4x^2+4xy+y^2=49\\ 4x^2-4xy+y^2=81\end{array}$

$\{\begin{array}{l}(2x+y{)}^2=49\\ (2x-y{)}^2=81\end{array}$

1) $\{\begin{array}{l}2x+y=7\\ 2x-y=9\end{array}$

$\{\begin{array}{l}y=7-2x\\ 2x-7+2x=9\end{array}$

$\{\begin{array}{l}y=7-2x\\ 4x=16\end{array}$

$\{\begin{array}{l}x=4\\ y=-1\end{array}$

2) $\{\begin{array}{l}2x+y=-7\\ 2x-y=-9\end{array}$

$\{\begin{array}{l}y=-7-2x\\ 2x+7+2x=-9\end{array}$

$\{\begin{array}{l}y=-7-2x\\ 4x=-16\end{array}$

$\{\begin{array}{l}x=-4\\ y=1\end{array}$

3) $\{\begin{array}{l}2x+y=7\\ 2x-y=-9\end{array}$

$\{\begin{array}{l}y=7-2x\\ 2x-7+2x=-9\end{array}$

$\{\begin{array}{l}y=7-2x\\ 4x=-2\end{array}$

$\{\begin{array}{l}x=-\frac{1}{2}\\ y=8\end{array}$

4) $\{\begin{array}{l}2x+y=-7\\ 2x-y=9\end{array}$

$\{\begin{array}{l}y=-7-2x\\ 2x+7+2x=9\end{array}$

$\{\begin{array}{l}y=-7-2x\\ 4x=2\end{array}$

$\{\begin{array}{l}x=\frac{1}{2}\\ y=-8\end{array}$

Ответ: $(4;-1),(-4;1),(-\frac{1}{2};8),(\frac{1}{2};-8)$.

$\{\begin{array}{l}3x(3x-4y)+4y^2=64\\ 3x(3x+4y)+4y^2=16\end{array}$

$\{\begin{array}{l}9x^2-12xy+4y^2=64\\ 9x^2+12xy+4y^2=16\end{array}$

$\{\begin{array}{l}(3x-2y{)}^2=64\\ (3x+2y{)}^2=16\end{array}$

1) $\{\begin{array}{l}3x-2y=8\\ 3x+2y=4\end{array}$

$\{\begin{array}{l}6x=12\\ -4y=4\end{array}$

$\{\begin{array}{l}x=2\\ y=-1\end{array}$

2) $\{\begin{array}{l}3x-2y=-8\\ 3x+2y=-4\end{array}$

$\{\begin{array}{l}6x=-12\\ -4y=-4\end{array}$

$\{\begin{array}{l}x=-2\\ y=1\end{array}$

3) $\{\begin{array}{l}3x-2y=-8\\ 3x+2y=4\end{array}$

$\{\begin{array}{l}6x=-4\\ -4y=-12\end{array}$

$\{\begin{array}{l}x=-\frac{2}{3}\\ y=3\end{array}$

4) $\{\begin{array}{l}3x-2y=8\\ 3x+2y=-4\end{array}$

$\{\begin{array}{l}6x=4\\ -4y=12\end{array}$

$\{\begin{array}{l}x=\frac{2}{3}\\ y=-3\end{array}$

Ответ: $(2;-1),(-2;1),(-\frac{2}{3};3),(\frac{2}{3};-3)$.