1. **State the problem:** Given the system of equations: $$a x + b y + c z = j$$ $$d x + e y + f z = k$$ $$g x + h y + i z = l$$ We want to solve for $x$, $y$, and $z$ using Gauss Elimination. 2. **Express $z$: ** To isolate $z$, we first focus on eliminating $x$ and $y$ from two equations to find $z$. Usually, $z$ is found by solving the last equation after elimination steps, but as per the problem, the main focus is showing $y$ and $x$ in terms of $z$. $z$ remains as a parameter here. 3. **Solve for $y$: ** From the first two equations, multiply the first equation by $d$ and the second by $a$ to eliminate $x$: $$d(a x + b y + c z) = d j$$ $$a(d x + e y + f z) = a k$$ Expanding: $$a d x + b d y + c d z = d j$$ $$a d x + a e y + a f z = a k$$ Subtract the second from the first: $$b d y - a e y + c d z - a f z = d j - a k$$ Factor: $$(b d - a e) y + (c d - a f) z = d j - a k$$ Isolate $y$: $$y = \frac{d j - a k - z (c d - a f)}{b d - a e}$$ 4. **Solve for $x$: ** From the first equation: $$a x = j - b y - c z$$ Divide both sides by $a$: $$x = \frac{j - b y - c z}{a}$$ **Final expressions:** $$z = z$$ $$y = \frac{d j - a k - z (c d - a f)}{b d - a e}$$ $$x = \frac{j - b y - c z}{a}$$