✔ 最佳答案
1.
y = x² - 4x + 3...... [1]
y = 1 - x ...... [2]
將 [1] 代入 [2] 中:
1 - x = x² - 4x + 3
x² - 3x + 2= 0
(x - 1)(x - 2) = 0
x = 1 或 x =2
代入 [2] 中:
當 x = 1: y = 1 - 1 所以 y = 0
當 x= 2: y = 1 - 2 所以 y = -1
答案: x = 1, y = 0 或 x = 2, y = -1
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2.
y = 2x² - 3x + 1...... [1]
17x + 2y + 5 = 0 ...... [2]
由 [2]:
y = (-17x - 5)/2 ...... [3]
將 [3] 代入 [1] 中:
(-17x - 5)/2 = 2x² - 3x + 1
-17x - 5 = 2(2x² - 3x + 1)
-17x - 5 = 4x² - 6x + 2
4x² + 11x+ 7 = 0
(4x + 7)(x + 1) = 0
x = -7/4 或 x= -1
代入 [3] 中:
當 x = -7/4: y = [-17(-7/4) - 5]/2 所以 y = 99/8
當 x = -1: y = [-17(-1) - 5]/2 所以 y = 6
答案: x = -7/4, y = 99/8 或 x = -1, y = 6
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3.
y = -x² - 7x + 5...... [1]
-x + 10 = y ...... [2]
將 [2] 代入 [1] 中:
-x + 10 = -x² - 7x + 5
x² +6x + 5 =0
(x + 1)(x + 5) = 0
x = -1 或 x= -5
代入 [2] 中:
當 x = -1: y = -(-1) + 10 所以 y = 11
當 x= -5: y = -(-5) + 10 所以 y = 15
答案: x = -1, y = 11 或 x = -5, y = 15
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4.
y = x² - 4x + 2 ...... [1]
-5x - y = -8 ...... [2]
由 [2]:
y = -5x + 8 ...... [3]
將 [3] 代入 [1] 中:
-5x + 8 = x² - 4x + 2
x² + x - 6 = 0
(x + 3)(x - 2) = 0
x = -3 或 x= 2
代入 [3] 中:
當 x = -3: y = -5(-3) + 8 所以 y = 23
當 x= 2: y = -5(2) + 8 所以 y = -2
答案: x = -3, y = 23 或 x = 2, y = -2
2015-05-22 05:47:50 補充:
一條方程式、兩個未知數。最後三題問甚麼?
2015-05-22 10:47:26 補充:
當 x = -7/4:
y = [-17(-7/4) - 5]/2
y = [(119/4) - (20/4)]/2
y = (99/4)/2
y = 99/8
2015-05-22 10:47:40 補充:
當 x = -7/4:
y = [-17(-7/4) - 5]/2
y = [(119/4) - (20/4)]/2
y = (99/4)/2
y = 99/8
2015-05-22 11:02:51 補充:
1. y = (x + 1)² - 1
(i) 頂點坐標 = (-1, -1)
(ii) 對稱軸: x + 1 = 0
(iii) 當x = 0: y = 1² - 1 所以 y截距 = 0
2. y = -2(x + 1)² + 3
(i) 頂點坐標 = (-1, 3)
(ii) 對稱軸: x + 1 = 0
(iii) 當x = 0: y = -2(1)² + 3 所以 y截距 = 1
2015-05-22 11:05:10 補充:
3. y = -3x² + 18x - 20
y = -3(x² - 6x + 9) + 27 - 20
y = -3(x - 3)² + 7
(i) 頂點坐標 = (3, 7)
(ii) 對稱軸: x - 3 = 0
(iii) 當x = 0: y = -3(-3)² + 7 所以 y截距 = -20
續題(1),每題只有一條方程式,但有兩個未知數,故方程式有無限個解。