\[ x + y = 5 \] \[ 2x - y = 3 \]
We can use elimination by multiplying 2 times the first row and subtracting it from the second row to get:
\[ x + y = 5 \] \[ -3y = -7 \] so y = 7/3 and then via back substitution x = 8/3
We can verify this in R:
A <- rbind(c(1, 1),
c(2, -1))
b <- rbind(5, 3)
x <- solve(A, b)
print(x)## [,1]
## [1,] 2.666667
## [2,] 2.333333