已知2x+5y+4z=15,7x+y+3z=14,则4x+y+2z的值为_.

问题描述:

已知2x+5y+4z=15,7x+y+3z=14,则4x+y+2z的值为______.

由于2x+5y+4z=15,7x+y+3z=14;令4x+y+2z=m(2x+5y+4z)+n(7x+y+3z)=(2m+7n)x+(5m+n)y+(4m+3n)z;由于左边=右边,则可列方程组2m+7n=45m+n=14m+3n=2;解得:m=111n=611.因此4x+y+2z=m(2x+5y+4z)+n(...