Question

求方程组　2分之x+y+3分之x-y＝1 　　　　（x+y）-5(x-y)=2

Answer 1

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

(x + y) = 5(x - y) + 2
3(x + y) = 15(x - y) + 6

3(x + y) + 2(x - y) = 6
15(x - y) + 6 + 2(x - y) = 6
17(x - y) = 0
x - y = 0
x = y

(x + x)/2 = 1
2x = 2
x = 1

x = y = 1

Answer 2

{(x+y)/2+(x-y)/3=1
{{x+y)-5(x-y)=2
原方程化为
{5x+y=6 ①
{2x-3y=-1 ②
①×3得15x+3y=18 ③
②+③得17x=17
x=1
把 x=1代入①得y=1
所以原方程组的解是
{x=1
{y=1

Answer 3

设
x+y=m
x-y=n
即
m/2 + n/3 =1 3m +2n =6
m-5n=2 3m-15n=6
解得
m=2
n=0

即
x-y=0
x+y=2

解得
x=1
y=1