【方法体验】已知方程组
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%7B%3C%2Fmo%3E%3Cmrow%3E%3Cmtable%3E%3Cmtr%3E%3Cmtd%3E%3Cmrow%3E%3Cmn%3E2018%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E2017%3C%2Fmn%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E20%3C%2Fmn%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmtext%3E%E2%91%A0%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmrow%3E%3Cmn%3E2019%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E2018%3C%2Fmn%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E500.%3C%2Fmn%3E%3Cmtext%3E%E2%91%A1%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
求4037x+y的值.小明同学发现解此方程组代入求值很麻烦!后来他将两个方程直接相加便迅速解决了问题.请你体验一下这种快捷思路,写出具体解题过程:
【方法迁移】根据上面的体验,填空:
已知方程组
则3x+y-z=.
【探究升级】已知方程组
求-2x+y+4z的值.小明凑出
“-2x+y+4z=2•(x+2y+3z)+(-1)•(4x+3y+2z)=20-15=5”,虽然问题获得解决,但他觉得凑数字很辛苦!他问数学老师丁老师有没有不用凑数字的方法,丁老师提示道:假设-2x+y+4z=m•(x+2y+3z)+n•(4x+3y+2z),对照方程两边各项的系数可列出方程组
, 它的解就是你凑的数!
根据丁老师的提示,填空:
2x+5y+8z=(x+2y+3z)+(4x+3y+2z)
【巩固运用】已知2a-b+kc=4,且a+3b+2c=-2,当k为时,8a+3b-2c为定值,此定值是.(直接写出结果)