7.3B – Solving with Gauss Elimination

• GOAL: Create Row echelon form and solve with back substitution.

• Row operations to create Row echelon form– 1.) Switch any 2 equations– 2.) Multiply any equation by a #≠0 ( or ÷)– 3.) Multiply an equation by a # and ADD to another equation. The SUM will REPLACE one of the 2 equations you added.

Hints: General Steps to Gauss Elim. (may vary if variables missing)

• 1.) Switch 2 equations so TOP equation has all 3 letters and a leading coefficient of “1” ( equation if needed)

• 2.) Use EQ1 & EQ2: Eliminate x: result = new EQ2• 3.) Use EQ1 & EQ3: Eliminate x: result = new EQ3• 4.) Use NEW EQ2 & NEW EQ3: Eliminate y: result =

new EQ3• 5) Multiply or divide to get all leading coefficients of

1 (reduced row echelon) or just solve EQ3 for z and back substitute from row echelon form.

Example: Solve with Gauss Elimination

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Example: Solve using Gauss Elimination

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Example: Solve with Gauss Elimination

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