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第四章:部分分式 Partial Fraction

第六章:角的形成及单位 Angles and Measurements

第十三章: 方程组 Simultaneous Equations

第十五章:二元一次不等式及线性规划 linear inequality in two variables and linear programming

13.2 方程组 Simultaneous Equations

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}

Answer:

无解

(2)

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

Answer:
(\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}

Answer:
(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}

Answer:
(\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}

Answer:
(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}

Answer:
(3, -2), (-3, 2), (-1\frac{2}{3}, 2\frac{2}{3}), (1\frac{2}{3}, -2\frac{2}{3})