Final answer:
The correct answer for the given question is option B. To solve the system of equations x+2y=3 and 3x+6y=9 using the graphical method, we can rearrange each equation in slope-intercept form and plot the lines on a graph. Since the lines are parallel, there is no solution.
Step-by-step explanation:
To solve the system of equations x+2y=3 and 3x+6y=9, we can use the graphical method. First, we need to rearrange each equation in slope-intercept form, which is y = mx + b. In the first equation, x+2y=3, we can subtract x from both sides to get 2y = -x + 3, and then divide by 2 to get y = -0.5x + 1.5. In the second equation, 3x+6y=9, we can divide both sides by 3 to get x + 2y = 3, and then subtract 2y from both sides to get x = -2y + 3.
Next, we can plot the two lines on a graph and see where they intersect. The intersection point represents the solution to the system of equations. In this case, the two lines are parallel, and they will never intersect. Therefore, the system of equations has no solution.