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Beginning Pre-Calculus for Game Developers by Boris Meltreger, John P. Flynt

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An Infinite Number of Solutions

If an inconsistent system has no solutions, another type of system, known as a dependent system, possesses an infinite number of solutions. The reason this occurs is that when you evaluate such systems, you find that you can express one variable in terms of the other. You have at hand such a system when you can multiply one of the equations in the system by some value that produces an equation that is the same as the other equation in the system. Equations that possess such a relationship with each other are known as dependent equations. To see how this can happen, consider this system of equations:

4x + 6y = 2

8x + 12y = 4

To make it easier to work with the two equations, reverse them:

8x + 12y = 4

4x + 6y = ...

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