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# What is the difference between solving simultaneous equations algebraically and graphically?

By Jack Putt on the 11th of June, 2012

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The graph will give you an approximate solution.

The algebra will give you an exact solution.

The reason for this is that the accuracy of the graph is not sufficient to home in on the exact solution.

an example:

x^2 + y^2 = 64
y = 4

solve this algebraically and you will see that the solution is:

x = +/- 6.92820323

solve this graphically and you will see that the solution lies somewhere around that value, but there's no way you can get it right on unless you zero in to a very minute detail which is not possible with most graphing software that might be available to you.

the exact solution is subject to the vagaries of the accuracy of the graphing software that you use.

here's the solution on the algebra.com graphing software.

can see that the points of intersection are somewhere around x = +/- 7 but there's no way you can see that the actual solution is +/- 6.92820323.

The graphing solution is good to give you a general idea of where your solution lies, or if you even have a solution.

To get the exact solution,  need to go to the algebraic solution.

By brindhamadhu on the 19th of January, 2013