1. **Stating the problem:** We have a system of linear equations: $$ ax + by + cz = j \\ dx + ey + fz = k \\ gx + hy + iz = l $$ We want to find expressions for $z$, $y$, and $x$ using Gauss Elimination. 2. **Eliminate variables to find $z$: ** - The coefficients form matrices that we manipulate. Gauss elimination reduces the system stepwise. 3. **Deriving $z$: ** Given the relation: $$ z = \frac{(bg - ah)(dj - ak) - (bd - ae)(gj - al)}{(bg - ah)(cd - af) - (bd - ae)(cg - ai)} $$ This comes from applying elimination on the coefficients and constants, solving the resulting simplified equations for $z$. 4. **Deriving $y$: ** Using $z$ above, substitute in the simplified second equation to isolate $y$: $$ y = \frac{1}{bd - ae}\left[(dj - ak) - z(cd - af)\right] $$ This expression shows the direct dependency of $y$ on $z$ and the constants. 5. **Deriving $x$: ** Finally, from the first equation, express $x$ in terms of $y$ and $z$: $$ x = \frac{1}{a}[j - yb - zc] $$ This completes the solution using Gaussian elimination. All steps use the linear manipulation of equations and substitution arriving at these formulas.