System of Equations Using Elimination. A System of Equations: Consists of two linear equations We want to find out information about the two lines: –T–The.

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Presentation transcript:

System of Equations Using Elimination

A System of Equations: Consists of two linear equations We want to find out information about the two lines: –T–The exact location (x, y) where they cross –I–If the two equations are the same line (infinite solutions) –I–If they are parallel, then they don’t cross (no solution)

One solution at a point (x, y) Consistent & independent Same line --- infinite solutions Consistent & dependent Parallel lines never cross---- no solution inconsistent 3 different possible outcomes

Ex 1 1.Check to see if one of the variables will cancel each other out. 2.If yes, add the two equations together and solve for the variable that is left. 3.Plug in that variable into one of the original equations and solve. Answer: (-1, -2)

Ex 2 1.Check to see if one of the variables will cancel each other out. 2.If yes, add the two equations together and solve for the variable that is left. 3.Plug in that variable into one of the original equations and solve. Answer: (5, 8)

Ex 3 1.Check to see if one of the variables will cancel each other out. 2.If yes, add the two equations together and solve for the variable that is left. 3.Plug in that variable into one of the original equations and solve. Answer: (-3, 2)

Ex 4 Solve for x 1.Check to see if one of the variables will cancel each other out. 2.If they won’t… multiply one or both equations by number(s) that will cause the variable to cancel. 3.If yes, add the two equations together and solve for the variable that is left. Answer: X=-7/13 Solving for ‘x’ Means to cancel The y’s

Ex 5 Solve for y 1.Check to see if one of the variables will cancel each other out. 2.If they won’t… multiply one or both equations by number(s) that will cause the variable to cancel. 3.If yes, add the two equations together and solve for the variable that is left. Answer: y=-7/10 Solving for ‘y’ Means to cancel The x’s

Ex 6 Solve for y 1.Check to see if one of the variables will cancel each other out. 2.If they won’t… multiply one or both equations by number(s) that will cause the variable to cancel. 3.If yes, add the two equations together and solve for the variable that is left. Answer: y=-17/10 Solving for ‘y’ Means to cancel The x’s

Ex 7 Answer: (5, -2) Let’s eliminate The y’s Now plug 5 in place of x in One of the equations