N2022 P1 Q1

Do not use a calculator in answering this question.

The complex numbers \(z\) and \(w\) satisfy the following equations.

\[\mathrm{i}z+2w=-1\]

\[(2-\mathrm{i})z+\mathrm{i}w=6\]

Find \(z\) and \(w\), giving your answers in the form \(a+\mathrm{i}b\) where \(a\) and \(b\) are real numbers.[4]