Title: Substitution Method

This system is most useful for systems of 2 equations in 2 unknowns. The essential idea here is that we solve one of the equations for one of the unknowns, and then substitute the result into the other equation.

Example: Consider the system

2x + 3y = 5

x + y = 5

Solve the second equation for x; this gives x = 5 - y. Then substitute this instead of x into the first equation and solve the resulting equation for y:

2 ( 5 - y) + 3y = 5

10 - 2y + 3y = 5

10 + y = 5

y = -5

Going back to the solution for x in the previous equation, we now see that x = 5 - (-5) = 10. Thus there is a unique solution to this equation and it is (x, y) = (10, -5).

Facts:

1. It does not matter which equation we choose first and which second. Just choose the most convenient one first!

2. It does not matter which unknown we choose first and which second. Again, just choose the most convenient one first.

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