x + y - z = -1
x - y - z = -1
z = 2
a <- matrix(c(1, 1, 0, 1, -1, 0, -1, -1, 1), nrow=3)
a
## [,1] [,2] [,3]
## [1,] 1 1 -1
## [2,] 1 -1 -1
## [3,] 0 0 1
b <- matrix(c(-1, -1, 2), nrow=3)
b
## [,1]
## [1,] -1
## [2,] -1
## [3,] 2
solve(a,b)
## [,1]
## [1,] 1
## [2,] 0
## [3,] 2
Therefore, x = 1, y = 0, z = 2.