ax+(a+m)y=a+2m,bx+(b+m)y=b+2m怎么解

Question

ax+(a+m)y=a+2m,bx+(b+m)y=b+2m怎么解

Answer 1

ax+(a+m)y=a+2m,①
bx+(b+m)y=b+2m.②
用加减消元法,并加以讨论：
①*b-②*a,得
[b(a+m)-a(b+m)]y=b(a+2m)-a(b+2m),
m(b-a)y=2m(b-a),
(1)m=0时y为任意数,由①,②,a,b不全为0时x=1-y.
(2)a=b时①,②同解,本题有无穷多解.
（3）m(b-a)≠0时y=2,
代入①,ax=-a,
(i)a=0时x为任意数,本题有无穷多解.
（ii)a≠0时x=-1,
∴{x=-1,
{y=2.