Solving Systems with Three Variables, Exercises of Linear Algebra

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3.4 Solving Systems with Three Variables xy 2 5 (2,1, 6) Is this a solution’ xby-2=-3 pleat ato aw-ytz AW equachons gx ty — z to see Fit mates Wie s bbernents 3.4 Solving Systems with Three Variables The solution is either 1. an ordered triple (x,y,z) 2. infinitely many solutions 3. no solutions Process for solving You need a plan. You need to write the plan down. You need to follow the plan + 1 Combine two equations to eliminate a ‘smart’ variable * 2™ Combine two different equations to eliminate the SAME SMART VARIABLE * 3 You will be left with a 2X 2 - Eliminate a ‘smart’ variable using either substitution or combination. ox+y4z=14 Bx -2y +32 = 210 O + to \oezy d X43y- B11 Bre Ay-3e 233 Taxnyezes AGpayszesat So otig® «er ee {Or Bye Cu)=10 > B4x- DWysh Bye 1D Sy aye Te eS “Hysuy “ i) B BG)+b)ue-4 4-H+eet &\ When you're in Albuquerque... 1. Make sure you copied the problem correctly. 2, Make sure you multiplied the entire equation. 3. Watch out for negatives. 4, Sometimes its better to abandon ship.