Solve by Cramers rule `x+y+z=6` `x-y+z=2` `3x+2y-4z=-5`

Explanation

`Delta = |{:(1,,1,,1),(1,,-1,,1),(3,,2,,-4):}|=|{:(1,,0,,0),(1,,-2,,0),(3,,-1,,-7):}|=14`
`Delta_(x) = |{:(6,,1,,2),(2,,-1,,1),(-5,,2,,-4):}|=|{:(6,,1,,1),(-4,,-2,,0),(19,,6,,0):}|=14`
`Delta_(y) = |{:(1,,6,,1),(1,,2,,1),(3,,-5,,-4):}|=|{:(1,,6,,1),(0,,-4,,0),(0,,-23,,-7):}|=28`
` " and "Delta_(z) = |{:(1,,1,,6),(1,,-1,,2),(3,,2,,-5):}|=|{:(1,,1,,6),(0,,-2,,-4),(0,,-1,,-23):}|=42`
Hence by Cremer's rule
` x=(Delta_(x))/(Delta) =1, y=(Delta_(y))/(Delta) =2, z=(Delta_(z))/(Delta)=3`