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equation which is always true, called an identity, or an equation which is never true, called a
contradiction. (If c = 0, then we get 0 = 0, which is always true. If c = 0, then we’d have
0 = 0, which is never true.) Even though identities and contradictions have a large role to play
Critics may argue that x = 5 is clearly an equation in one variable. It can also be considered an equation in 117
variables with the coeﬃcients of 116 variables set to 0. As with many conventions in Mathematics, the context will
clarify the situation. 450 Systems of Equations and Matrices in the upcoming sections, we do not consider them linear equations. The key to identifying linear
equations is to note that the variables involved are to the ﬁrst power and that the coeﬃcients of the
variables are numbers. Some examples of equations which are non-linear are x2 + y = 1, xy = 5 and
e2x + ln(y ) = 1. We leave it to the reader to explain why these do not satisfy Deﬁnition 8.1. From
what we know from Sections 1.2 and 2....
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