13x+14y=41 14x+13y=40

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13x+14y=4114x+13y=4013x+14y=4114x+13y=4013x+14y=4114x+13y=4013x+14y=41将整个式子乘以1414x+13y=40将整个式子乘以13得:

13x+14y=41 14x+13y=40
13x+14y=41 14x+13y=40

13x+14y=41 14x+13y=40
13x+14y=41 将整个式子乘以14
14x+13y=40将整个式子乘以13
得:182x+196y=574
182x+169y=520
上式减下式,得27y=54 y=2 所以x=1

13x+14y=41 ~(1)
14x+13y=40 ~(2)
(1) - (2): -x + y = 1 ~(3)
(3) * 13: -13x + 13y = 13 ~(4)
(1) + (4): 27y = 54
得 y = 2
所以 x = 1
答: x = 1, y = 2

13x+14y=41
14x+13y=40
上两式相加得27X+27Y=81
X+Y=3
X=3-Y
代入第一式
13(3-Y)+14Y=41
39-13Y+14Y=41
Y=2
X=1