System of Equations Using Elimination

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

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

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

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

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

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

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

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

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