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**Unformatted text preview: **Chapter 4 Solving Systems of Linear Equations and Inequalities 4.1 Solving Systems of Linear Equations by Graphing Martin-Gay, Beginning and Intermediate Algebra, 4ed 3 Systems of Linear Equations A system of linear equations consists of two or more linear equations. This section focuses on only two equations at a time. The solution of a system of linear equations in two variables is any ordered pair that solves both of the linear equations. Martin-Gay, Beginning and Intermediate Algebra, 4ed 4 Determine whether the given point is a solution of the following system. point: ( 3, 1) system: x y = 4 and 2 x + 10 y = 4 Plug the values into the equations. First equation: 3 1 = 4 true Second equation: 2( 3 ) + 10( 1 ) = 6 + 10 = 4 true Since the point ( 3, 1) produces a true statement in both equations, it is a solution. Solution of a System Example : Martin-Gay, Beginning and Intermediate Algebra, 4ed 5 Determine whether the given point is a solution of the following system point: (4, 2) system: 2 x 5 y = 2 and 3 x + 4 y = 4 Plug the values into the equations. First equation: 2( 4 ) 5( 2 ) = 8 10 = 2 true Second equation: 3( 4 ) + 4( 2 ) = 12 + 8 = 20 4 false Since the point (4, 2) produces a true statement in only one equation, it is NOT a solution. Solution of a System Example : Martin-Gay, Beginning and Intermediate Algebra, 4ed 6 Since a solution of a system of equations is a solution common to both equations, it would also be a point common to the graphs of both equations....

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