Final answer:
The solution to a system of equations can be found graphically, with possible results including a single solution, infinite solutions, or no solution. These correspond to graphs that intersect at a point, coincide as a line, or are parallel. Analytical methods offer more accuracy than graphical methods.
Step-by-step explanation:
The solution to a system of equations can be understood by looking at the graphical representation of the equations. When graphing each equation on a coordinate plane, the point(s) where their graphs meet represent the solution(s) to the system. There are three possibilities:
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- Single Solution: The graphs intersect at exactly one point. The coordinates of this point represent the unique solution to the system.
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- Infinite Solutions: The graphs coincide, meaning they are the same line. This indicates that the system has an infinite number of solutions, as every point on the line satisfies both equations.
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- No Solution: The graphs are parallel and do not intersect, which means there is no solution to the system since no single point satisfies both equations.
Solving systems of equations analytically can be more accurate than graphical techniques as it involves precise calculations, while graphing can be subject to interpretation and drawing inaccuracies.