高级数学 | 高一下册 | 13.2 方程组 Simultaneous Equations - 独中课程 | 线上补习

高中一 | 高级数学

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13.2 Simultaneous Equations 方程组

Solve the following simultaneous equations :

解下列方程组：

(1)

$\begin{cases} 2x^2 - xy + 3y^2 - y + 1 = 0 \\ 4x^2 - 2xy -y^2 + 2 = 0 \end{cases}$

无解

(2)

$\begin{cases} 2x^2 - 4xy - 2y^2 + 3x + 3y + 4 = 0 \\ x^2 - 2xy -y^2 + y + 2 = 0 \end{cases}$

( $\frac{1}{2}$ , $-1\frac{1}{2}$ ), (-2, 6)

(3)

$\begin{cases} x^2 + 2x + 2y = y^2 \\ x^2 + y^2 = 8 \end{cases}$

(2, -2), (-2, 2), (-1 + $\sqrt3$ , 1 + $\sqrt3$ ), (-1 – $\sqrt3$ , 1 – $\sqrt3$ )

(4)

$\begin{cases} 4x^2- 7xy- 2y^2 + 7x + 4y- 2 = 0 \\ 2x^2 + xy - y^2 = 0 \end{cases}$

( $\frac{1}{6}$ , $\frac{1}{3}$ ) ,

( $\frac{2}{3}$ , $\frac{4}{3}$ ) ,

( $-\frac{2}{3}$ , $\frac{2}{3}$ ) ,

( $\frac{1}{3}$ , $-\frac{1}{3}$ ) .

(5)

$\begin{cases} 3x^2 + xy + y^2 - 15 = 0 \\ x^2 + 5xy + 16y^2 - 30 = 0 \end{cases}$

(2, 1), (-2, -1), (2.32, -1.65), (-2.32, 1.65)

(6)

$\begin{cases} 4xy + x^2 = - 15 \\ -2xy + y^2 = 16 \end{cases}$

(3, -2), (-3, 2), (-1 $\frac{2}{3}$ , 2 $\frac{2}{3}$ ), (1 $\frac{2}{3}$ , -2 $\frac{2}{3}$ )