1. **State the problem:** We are given the system of linear equations: $$2x - 3y = 1$$ $$6x - 9y = 3$$ and we need to find the parametric equations describing its solution set. 2. **Check for infinite solutions:** Notice the second equation is a multiple of the first: $$6x - 9y = 3 \implies 3(2x - 3y) = 3 \implies 2x - 3y = 1$$ So both equations represent the same line, meaning infinitely many solutions. 3. **Express one variable in terms of the other:** From the first equation: $$2x - 3y = 1$$ Solve for $x$: $$2x = 1 + 3y$$ $$x = \frac{1 + 3y}{2}$$ 4. **Parametrize the solution:** Let $y = t$ (parameter), then $$x = \frac{1 + 3t}{2}$$ 5. **Write parametric equations:** $$\boxed{\begin{cases} x = \frac{1 + 3t}{2} \\ y = t \end{cases}}$$ where $t$ is any real number. This describes all solutions to the system. Final answer: $$x = \frac{1 + 3t}{2}, \quad y = t, \quad t \in \mathbb{R}$$