Final answer:
Solving a linear system graphically involves finding the point of intersection between two lines on a graph, but it's less precise than analytical methods due to limitations in scale and precision of the graphing tool. Analytical methods provide an exact solution, while graphical methods might require estimation.
Step-by-step explanation:
When solving a linear system graphically, the main goal is to find the point of intersection between the lines represented by each equation in the system. If the equations are in the standard y = mx + b form, where m is the slope and b is the y-intercept, we can plot both lines on the same graph.
However, the analytical technique, typically involving algebraic methods such as substitution or elimination, is potentially more accurate than the graphical technique. This is because when you solve a system graphically, you're limited by the scale and precision of the graph. Even if data from the graphs is assumed accurate to three digits, it's impossible to pinpoint the exact location of the intersection to the same degree of precision as analytical methods.
For instance, if the intersection point has irrational coordinates or if it's between two grid lines, estimating the precise values can be challenging. In contrast, using the analytical technique will usually result in an exact solution, provided no rounding or estimation is involved. Moreover, if you were to determine graphically the intersection point and the grid lines are very close together, you may need to zoom in significantly to improve your estimate, which is not as straightforward as solving the system analytically.