SYSTEMS OF LINEAR EQUATIONS FRIDAY, SEPTEMBER 5, 2014.

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Presentation transcript:

SYSTEMS OF LINEAR EQUATIONS FRIDAY, SEPTEMBER 5, 2014

WHAT IS A SYSTEM OF LINEAR EQUATIONS? A system of linear equations is 2 or more equations with the same variables. To solve a system of equations, you must find the ordered pair that satisfies all of the equations.

VOCABULARY Consistent – has at least 1 solution Inconsistent – has no solution Independent – has exactly 1 solution Dependent – has infinite solutions (all real numbers)

SOLVING SYSTEMS BY GRAPHING 1.Solve all equations for y. 2.Graph all equations on the same graph. 3.The lines: a.Intersect b.Are parallel c.Are the same line 4.Write the solution: a.Point of intersection b.No solution c.All real numbers

EXAMPLES Solve using graphing: y = 6 - x -x + y = 4

SOLVING SYSTEMS BY SUBSTITUTION 1.Solve for one variable. 2.Substitute your solution into a different equation. 3.Solve for the second variable. 4.Substitute your answer back into your equation in number 1. 5.Write the solution. (ordered pair, no solution, or all real numbers)

EXAMPLES Solve using substitution: y = 6 - x -x + y = 4

SOLVING SYSTEMS BY ELIMINATION 1.Determine if you should use: a.Addition b.Subtraction c.Multiplication 2.If a.Addition – add the equations together b.Subtraction – subtract the equations c.Multiplication – multiply one equation, then add them together 3.Substitute your answer back into an original equation. 4.Write the solution. (ordered pair, no solution, or all real numbers)

EXAMPLES Solve using elimination: y = 6 - x -x + y = 4

CLASSWORK p. 146 Start with #20 and work backwards to #11

HOMEWORK 1.2x + y = -3 6x + 3y = x – 2y = -1 8y = x 3.5x + y = 10 4x + y = 4 Solve using your preference: 1.Graphing 2.Substitution 3.Elimination