All three methods will result in approximately the same solution. However, sometimes there might be some differences. Let's take a look at each method.
Systems Created From a Graph
A system of equations created from a graph may not be as exact if specific points are not determined. Let's see an example.
We cannot determine the exact coordinates of the point of intersection of the above lines. Also, we cannot determine an exact value for the slopes or the y-intercepts of the lines. Therefore, the solution will be approximated.
Systems Created From a Table of Values
Sometimes, the values on a table might not be exact either. They might be approximations of the actual values. For example, distances between cities could be approximated to the nearest mile.
Distance Between New York and Other Cities (to the nearest mile)
Paris
3637 miles
London
3459 miles
Warsaw
4256 miles
Mexico City
2643 miles
Buenos Aires
5295 miles
If we use some of the information above to construct a system of equations, our result will not be exact. Since the distances are approximated to the nearest mile, our result will also be an approximation.
Systems Created From Verbal Descriptions
Sometimes verbal descriptions are not accurate, and therefore they do not lead to an exact answer. Let's consider an example.
"The sum of the heights of Jacob and Henrik
isaround3.6meters. The difference isaround
0.2meters. Find the height of the two men."
Note that exact values are not provided. This means that the system created from the above description will produce an approximated solution.
Conclusion
In conclusion, if the verbal description, graph, or table provide exact information, an exact answer can be obtained. Conversely, if they provide approximations, we cannot obtain an exact answer. Instead, we get an approximated answer.
