【方法体验】已知方程组
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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)