中ニ..有六條數吾識(消元/代入法解聯立方程)

1:以消元法解聯立方程
X+Y=5.......(1)
2X+3Y=10......(2)
(2) * 2 => 2X + 2Y = 10 ... (3)
(2) - (3) => Y = 0
代入(1), X + 0 = 5 => X = 5
2:以消元法解聯立方程
2X+5Y=5......(1)
X+3Y=3......(2)
(2) * 2 => 2X + 6Y = 6 ... (3)
(3) - (1) => Y = 1
代入(2), X + 3 = 3 => X = 0
3:以代入法解聯立方程
X+Y=1.....(1)
X-2Y=4....(2)
(1) => X = 1 - Y ...(3)
代入(2), (1-Y) - 2Y = 4
1 - 3Y = 4
-3Y = 3
Y = -1
代入(3), X = 1 - (-1) = 2
4:以代入法解聯立方程
X+Y=10.......(1)
3X-2Y=15....(2)
(1) => X = 10 - Y ... (3)
代入(2), 3(10 - Y) - 2Y = 15
30 - 3Y - 2Y = 15
-5Y = -15
Y = 3
代入(3), X = 10 - 3 = 7
5:以代入法解聯立方程
2X+3Y=2.....(1)
2X+Y=4.......(2)
(2) => Y = 4 - 2X ...(3)
代入(1) 2X + 3(4 - 2X) = 2
2X + 12 - 6X = 2
-4X = -10
X = 2.5
代入(3), Y = 4 - 2(2.5) = -1
6:以代入法解聯立方程
3X-Y=5.....(1)
2X+3Y=7....(2)
(1) => Y = 3X - 5 ...(3)
代入(2), 2X + 3(3X - 5) = 7
2X + 9X - 15 = 7
11X = 22
X = 2
代入(3), Y = 3(2) - 5 = 1

1. X+Y=5.......(1) => X = 5 - Y
2X+3Y=10......(2)
將(1)代入(2) 得
2(5-Y)+3Y=10
=> 10-2Y+3Y=10
=> 3Y-2Y=10-10
=> Y=0 而 X=5

2. 2X+5Y=5......(1)
X+3Y=3......(2) => X = 3 - 3Y
將(2)代入(1) 得
2(3-3Y)+5Y=5
=> 6-6Y+5Y=5
=> 6-5 = 6Y-5Y
=> Y=1 而 X=0

3. X+Y=1.....(1)
X-2Y=4....(2) => X=4+2Y
將(2)代入(1) 得
(4+2Y)+Y=1
=> 3Y=-3
=> Y=-1 而 X=2

4. X+Y=10.......(1) => X=10-Y
3X-2Y=15.....(2)
將(1)代入(2) 得
3(10-Y)-2Y=15
=> 30-3Y-2Y=15
=> 30-15=3Y+2Y
=> 15=5Y
=> Y=3 而 X=7

5. 2X+3Y=2.....(1)
2X+Y=4.......(2) => Y=4-2X
將(2)代入(1) 得
2X+3(4-2X)=2
=> 2X+12-6X=2
=> 12-2=6X-2X
=> 4X=10
=> X=2.5 而 Y= -1

6. 3X-Y=5.....(1) => -Y=5-3X => Y=3X-5
2X+3Y=7.....(2)
將(1)代入(2) 得
=> 2X+3(3X-5)=7
=> 2X+9X-15=7
=> 11X=22
=> X=2 而 Y=1

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