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Unformatted text preview: Chapter 2.1: Systems of Linear Equations A linear equation is an equation in which each variable has degree one. We call them linear because when a linear equation involves only two variables, the equation describes a straight line. Examples: Here are some examples of linear equations. 7 y + 3 x = 2 x + y + z = 7 7 a- 11 17 b + 72 3 c = 91 Here are some examples of nonlinear equations. x 2 + 5 x = 2 x- yz- w = 7 a 3- b 3 2 = 2 A system of linear equations is a collection of one or more linear equations. A solution of a system is a set of values which satisfies all of the equations in the system. Example: Verify that x = 1 and y = 2 form a solution for the following system. 2 x + 5 y = 12 2 x + 6 y = 14 We will look at the first equation, at the right and left sides separately, substituting in the given values for x and y . L.S. = 2(1) + 5(2) = 2 + 10 = 12 1 R.S. = 12 Since the left side is equal to the right side for the values x = 1 , y = 2, then we say that these values satisfy the first equation. We do the same for the second equation. L.S. = 2(1) + 6(2) = 2 + 12 = 14 R.S. = 14 The values also satisfy the second equation. Since the values x = 1 , y = 2 satisfy all of the equations in the system, then these...
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