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Linear Systems

Linear Systems

Linear Systems

In this chapter, we present systems of linear equations as groups of two or more linear equations that are analyzed and solved simultaneously. The solution set of a system of equations lies on the point (or points) at which every equation in the system is true. Systems of linear equations can have zero, one or infinitely many solutions, depending on the ways in which the lines relate.
A system with zero solutions consists of parallel lines. When a system consists of linear equations with different slopes, the system has one solution. Infinitely many solutions has a system of linear equations if the lines are coincidental, different versions of the same line.
We will in the chapter explore one graphical method and two algebraic methods of solving system of linear equations.
To solve linear systems graphically, we will find the point or points where the lines intersect. The algebraic methods are the Substitution Method and the Elimination Method. In the Substitution Method one of the variables in one of the equations is substituted for an equivalent expression. In the Elimination Method the two equations are combined in such a way that one of the variables is eliminated resulting is an equation with only one variable.
Finally, systems of linear inequalities and their solutions will be introduced.

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