Question

解方程组 3(X+Y)-5(X-Y)=16…………① 2(x+y)+(X-Y)=15…………②

Answer 1

2式两边同乘以5得3式10（X+Y)+5(X-Y)=75
1式+3式得13（x+y)=91则得4式X+Y=7
代入1式得5式X-Y=1
4式+5式得X=4
代入4式Y=3
于是方程组解为X=4 Y=3

Answer 2

3(X+Y)-5(X-Y)=16…………①
2(x+y)+(X-Y)=15…………②
设x+y=a x-y=b
则
3a-5b=16 ③
2a+b=15 ④
③+④×5得：
3a+10a=16+75
13a=91
∴a=7
b=1
∴x+y=7
x-y=1
∴x=4
y=3