Question

用适当的方法解下列方程(x+1)/2=(y+3)/4=(x+y)/5

Answer 1

(x+1)/2=(y+3)/4
2(x+1)=y+3
2x+2=y+3
2x=y+1
y=2x-1

(x+1)/2=(x+y)/5
5(x+1)=2(x+y)
5(x+1)=2(x+2x-1)
5x+5=2(3x-1)
5x+5=6x-2
6x-5x=5+2
x=7

y=2x-1=2*7-1=13

所以x=7,y=13

Answer 2

设(x+1)/2=(y+3)/4=(x+y)/5=k
则 x+1=2k x=2k-1 (1)
y+3=4k y=4k-3 (2)
x+y=5k (3)
(1)(2)代入(3)
6k-4=5k k=4
代入(1) x=2*4-1=7
代入(2) y=4*4-3=13

Answer 3

设(x+1)/2=(y+3)/4=(x+y)/5=k
那么x=2k-1,y=4k-3,x+y=5k
故x+y=(2k-1)+(4k-3)=5k
解得k=4
所以x=2*4-1=7，y=4*4-3=13

Answer 4

(x+1)/2=(y+3)/4
得2x+2=y+3 =>y=2x-1

(x+1)/2=(x+y)/5
代入得 5x+5=2(x+2x-1)
=>5x+5=6x-2
=>x=7

y=2x-1=13