聯立方程`

1.5x + 2y = 1 ...(1)
2y - x = 7 ...(2)


(2) => x = 2y - 7
代入(1), 5(2y - 7) + 2y = 1
10y - 35 + 2y = 1
12y = 36
y = 3
x = 2(3) - 7 = -1


(2) * 5 => 10y - 5x = 35 ...(3)
(1) + (3) => 12y = 36
y = 3
代入(1) 5x + 6 = 1 => x = -1


2.3s - 4t = 7 ...(1)
5s + t = 4 ...(2)


(2) => t = 4 - 5s
代入(1), 3s - 4(4 - 5s) = 7
3s - 16 + 20s = 7
23s = 23
s = 1
t = 4 - 5(1) = -1


(2)*4 => 20s + 4t = 16 ... (3)
(1)+(3) => 23s = 23
s = 1
代入(1), 3(1) - 4t = 7
3 - 7 = 4t
t = -1


3.5a - 2b = 11 ...(1)
3a +4b =17 ...(2)


(1) => 5a = 11 + 2b
a = (11 + 2b)/5
代入(2), 3(11 + 2b)/5 + 4b = 17
3(11 + 2b) + 20b = 85
33 + 6b + 20b = 85
26b = 52
b = 2
a = (11 + 4)/5 = 3


(1)*2 => 10a - 4b = 22 ... (3)
(2) + (3) => 13a = 39
a = 3
代入(1), 5(3) - 2b = 11
15 - 11 = 2b
b = 3