Linear Equations

Definition: This is an equation where the variables have 1 as their exponents. When plotted, this gives a straight line.

Example: Determine which of the following are linear equations.
2x + 5y = 7
4a = 7/b + 2
7m² – 2n = 3
4y= 7

Solution:

Step 1: Observe the powers of the variables.

2x + 5y = 7 ⇒ Linear, all exponents are 1.
4a = 7/b + 2 ⇒ Non-linear, exponents are 1 and -1.
7m² – 2n = 3 ⇒ Non-linear, exponents are 2 and 1.
4y = 7⇒ Linear, exponent is 1.

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