Substitution

Substitution is a way to solve a system when one equation already tells you what a variable equals. You replace that variable in the other equation with the expression it equals. In the system y = 2x - 1; x + y = 5, the first equation says that y equals 2x - 1. Replace y in the second equation with 2x - 1. The result is one equation with one variable:

x + (2x - 1) = 5

3x - 1 = 5

x = 2

Now put x = 2 into the first equation to find y: y = 2(2) - 1, so y = 3. The solution is the pair x = 2, y = 3. Substitution gives the exact point where the two lines cross, without drawing them.

Substitution is convenient when one equation already has a variable isolated. Replace that variable in the other equation with the expression it equals.