Prove: x ! y is logically equivalent to .:y/ ! .:x/.

Math121 Chapter 3 Lesson 3.2 – Linear Equations in Two Variables EXAMPLE 1. -2x + 11(x + 2y) = 11x + y (When solving linear equations with two variables, we want to get it in the proper form ax + bx = c. If we cannot get it into this form, it is not linear! Simple enough, right So first, distribute the 11 to the x and 2y.) -2x + 11x + 22y = 11x + y (Now combine like terms.) 9x + 22y = 11x + y (Now, subtract the terms with variables on the right side of the equation from the left side of the equation to get it in the proper form.) -2x + 21y = 0 (Yes! It’s linear. Yay.) EXAMPLE 2. (y + 3) – y = -5x + 1 (First, factor out the (y + 3) .) y + 6y + 9 – y = -5x + 1 (Now, combine like terms on like sides of the equation.) 6y + 9 = -5x + 1 (Subtract terms with variables on the right side of the equation from the left side of the equation.) 6y + 5x = -8 (Yes! It’s linear, because this is i