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Unit 5 - Objective 1 - Linear Equations

A linear equation is the equation of a straight line. An equation is linear if each term contains only one variable to the first power or the term is a constant.

Examples:

 2x + 7 = 20 is a linear equation in one variable, namely x. 3x - 4y = 5 is a linear equation in two variables, namely x and y. 4x + 3y - 2z = 5 is a linear equation in three variables, namely x, y, and z.

A solution is any set of numbers, one for each variable, which satisfies the equation.

Examples:

Given the linear equation 3x - 2y = 9
 1. Is x = - 3 y = 0 a solution? 3 (-3) - 2 (0) = 9 -9 - 0 = 9 - 9 9 No 2. Is x = 3 y = 0 a solution? 3 (3) - 2 (0) = 9 9 - 0 = 9 9 = 9Yes

There are many solutions that will satisfy this equation. If you are given a value for x you can determine the y value by solving the equation.

Examples:

 1. 3x - 2y = 9 plug in 1 for x x = 1 3 (1) - 2y = 9 3 - 2y = 9 -2y = 6 y = - 3 so (1, -3) is a solution 2. 3x - 2y = 9 plug in 0 for y y = 0 3x - 2 (0) = 9 3x - 0 = 9 3x = 9 x = 3 So (3, 0) is a solution

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