Past exam of the mathematical methods I course of the University of Oxford / 2017 resit / 5 / b / Solution

With $\alpha =\beta =6$, the eliminated equation gives $4y=3$. Back substitution yieldsThe three left-hand sides are respectively $4$, $2$ and $6$, verifying the solution in the original linear system. Its determinant is $-8\ne 0$, so this solution is unique.