Answer: C. I and II

Explanation:1. Understand conditions for at least one solution: A system of two linear equations has at least one solution if the lines are either intersecting (exactly one solution) or identical (infinitely many solutions). The system will have *no* solution only if the lines are parallel and distinct. Lines are parallel if they have the same slope but different y-intercepts. Lines are identical if they have the same slope and the same y-intercept. Lines are intersecting if they have different slopes.

2. Analyze the given equation: $6x+3y=5$. Let's find its slope by writing it in $y=mx+b$ form: $3y = -6x+5$ $y = -\dfrac{6}{3}x + \dfrac{5}{3}$ $y = -2x + \dfrac{5}{3}$. The slope of the given line is $m\_1 = -2$.

3. Analyze Equation I: $9x+4.5y=7.5$ Write it in $y=mx+b$ form: $4.5y = -9x+7.5$ Multiply by $2$ to clear decimals: $9y = -18x+15$ $y = -\dfrac{18}{9}x + \dfrac{15}{9}$ $y = -2x + \dfrac{5}{3}$. The slope of Equation I is $m\_I = -2$, and the y-intercept is $\dfrac{5}{3}$. Since Equation I has the same slope and same y-intercept as the given equation, the lines are identical. Identical lines have infinitely many solutions. Thus, the system has at least one solution. Statement I could be the other equation.

4. Analyze Equation II: $9x-4.5y=7.5$ Write it in $y=mx+b$ form: $-4.5y = -9x+7.5$ Multiply by $-2$ to clear decimals and change sign: $9y = 18x-15$ $y = \dfrac{18}{9}x - \dfrac{15}{9}$ $y = 2x - \dfrac{5}{3}$. The slope of Equation II is $m\_{II} = 2$. Since the slope of the given line ($m\_1 = -2$) is different from the slope of Equation II ($m\_{II} = 2$), the lines are intersecting. Intersecting lines have exactly one solution. Thus, the system has at least one solution. Statement II could be the other equation.

5. Determine which statements could be true: - Statement I leads to infinitely many solutions (which is "at least one solution"). - Statement II leads to exactly one solution (which is "at least one solution"). Therefore, both I and II could be the other equation in the system.

Conclusion:Both Equation I and Equation II could be the other equation in the system for it to have at least one solution. So the answer is I and II.