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How can graphs be used to estimate the solution for a system of linear equations?
Graphs can be used in the following way to estimate the solution of a system of liner equations. After you graph however many equations you have, the point of intersection will be your solution. However, reading the exact solution on a graph may be tricky, so that's why other methods (substitution and elimination) are preferred.
What is the exact solution to cosx equals x?
There is no "exact" solution. This type of equation falls into the category of transcendental equations, which generally don't have exact solution except in special cases. The approximate solution, however, is roughly 0.739085
What is the answer to The solution to this system of equations lies between the x-values -2 and -1.5. At which x-value are the two equations approximately equal?
To find the x-value where the two equations are approximately equal between -2 and -1.5, you would typically evaluate the two equations at various points in that range. By checking values or using methods such as graphing or numerical approximation (like the bisection method), you can determine the specific x-value where the equations intersect. Without specific equations provided, it's impossible to give an exact answer, but the solution lies in that interval.
Why is trial and error so useful in math?
There are many equations for which there is no method for obtaining an exact solution. In such circumstances, an efficient trial and error method may be the only way.
What are the differences between numerical solution method and analytical solution?
Analytical solution is exact, while a numeric solution is almost always approximate
