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

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Substitution

To solve a system of equations in a more systematic way, you use substitution. Toward this end, you first solve one of the equations in the system for one of its variables. You then substitute the solution into the other equation.

Here is a system of equations that you can solve in this way:

x + y = 12

3x + y = 4

To solve this set of equations through substitution, you can solve either equation for either variable. In this instance, begin by solving the first equation for y:

x + y = 12

y = 12 - x

You can then proceed to substitute the expression 12 - x into the second of the equations. To do so, you proceed as follows:

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