中五解聯立方程

(1) 2x + 2/y = 3 … (1)
3x + 5/y = 5 … (2)
(1)*3 => 6x + 6/y = 9 … (3)
(2) * 2 => 6x + 10/y = 10 … (4)
(4) – (3) => 4/y = 1
y = 4
代入(1) => 2x + 2/4 = 3
x = 5/4
(2) (x – 2) / 3 = (y – 1)/4 … (1)
(4x – 7y – 23)/6 = (y – 1)/4 … (2)
(1) => 4x – 8 = 3y – 3
8x – 6y = 10 … (3)
(2) => 4x – 7y – 23 = 1.5y – 1.5
4x – 8.5y = 21.5
8x – 17y = 43 … (4)
(3) – (4) => 11y = -33
y = -3
代入(3), 8x + 18 = 10
x = -1
(3) 設分子為x分母為y
(x + 1) / (y + 1) = 1/2 … (1)
x / (y + 3) = 1/4 … (2)
(1) => 2x + 2 = y + 1
y = 2x + 1 …(3)
(2) => 4x = y + 3
y = 4x – 3… (4)
(4) – (3) => 0 = 2x – 4
x = 2
代入(3), y = 5
該分數為 2/5
(4) y = x^2 – 2x – 3 … (1)
y = 3 – x … (2)
代(2)入(1), 3 – x = x^2 – 2x – 3
x^2 – x – 6 = 0
(x – 3)(x + 2) = 0
x = 3 或x = -2
x = 3 => y = 0
x = -2 => y = 5
(5) y = 9 + 2x – x^2 … (1)
y = -3x + 13 … (2)
代(2)入(1), -3x + 13 = 9 + 2x – x^2
x^2 – 5x + 4 = 0
(x – 1)(x – 4) = 0
x = 1或 x = 4
x = 1 => y = 10
x = 4 => y = 1