Question

解方程组{5/x-12/y=6,2/x+3/y=18时,如果设1/x=m,1/y=n,则 原方程

Answer 1

令m=1/(x+y),n=1/(x-y)

则方程组变为{15m+2n=5,10m+4n=-2}

解得{m=3/5,n=-2}

所以1/(x+y)=3/5,1/(x-y)=-2}

变形为{x+y=5/3,x-y=-1/2}

解得{x=7/12,y=13/12}