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Published byAbraham Briggs Modified over 7 years ago
SYSTEMS OF LINEAR EQUATIONS SUBSTITUTION AND ELIMINATION Objectives: Solve Systems of Equations by Substitution and Elimination Identify Inconsistent Systems of Equations containing two or three variables Solve Systems of Equations containing two or three variables
Systems of Linear Equations A collection of two or more linear equations in the form that are straight lines when graphed, each containing one or more variables with no exponents other than 1 Solution of a System of Linear Equations in two variables: Solution of a System of Linear Equations in two variables: an ordered pair that satisfies both equations in the system (Consistent),Inconsistent) A system of linear equations can have exactly one solution (Consistent), no solution (Inconsistent) or infinitely many solutions. The lines either intersect at one point, are parallel or are identical.
Methods to solve systems of equations Graphing Graphing: graph both of the equations in the same rectangular coordinate system. Find the solution to the linear system by locating the point Substitution: Substitution: solve either of the equations for one variable in terms of the other, substitute the expression into the other equation, solve for that variable and the other variable Elimination: Elimination: rewrite both equations in the form, multiply either equation or both equations by appropriate nonzero numbers so that the sum of one of the coordinates coefficients is 0, add the equations and solve for the variable and the other variable
EX: Solve the system of equations 1. 2.
EX: Solve the system of equations 3. 4.
EX: Solve the system of equations 5.
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