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CHAPTER_ppt_4_1 - Chapter 4 Solving Systems of Linear...

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Chapter 4 Solving Systems of Linear Equations and Inequalities
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§ 4.1 Solving Systems of Linear Equations by Graphing
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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.
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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 :
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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 :
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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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