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Mathematics

273Introduction to Systems of Linear Equations
274Solving Systems by Graphing: Basic Technique
275Types of Solutions: One, None, or Infinitely Many
276Graphing Systems with Parallel and Coincident Lines
277Introduction to the Substitution Method
278Substitution When One Equation is Already Solved
279Substitution Requiring Solving for a Variable First
280Identifying No Solution or Infinite Solutions via Substitution
281Comparing Graphing and Substitution Methods
282Application Problems Using Systems and Substitution
283Introduction to the Elimination Method
284Eliminating a Variable by Adding Equations
285Eliminating a Variable by Subtracting Equations
286Multiplying One Equation to Enable Elimination
287Multiplying Both Equations to Enable Elimination
288Choosing the Easier Variable to Eliminate
289Elimination with Fractions and Decimals
290Special Cases: No Solution and Infinite Solutions
291Word Problems Solved by Elimination
292Introduction to Three-Variable Systems
293Visualizing Three-Variable Systems
294Solving Three-Variable Systems by Elimination
295Choosing Strategic Pairs for Elimination
296Back-Substitution in Three Variables
297Inconsistent Three-Variable Systems
298Dependent Three-Variable Systems
299Applications of Three-Variable Systems
300Graphing Linear Inequalities in Two Variables
301Systems of Linear Inequalities
302Vertices of the Feasible Region
303Bounded vs Unbounded Feasible Regions
304Introduction to Linear Programming
305The Objective Function
306The Corner Point Theorem
307Solving Linear Programming Problems Graphically
308Applications: Maximization Problems
309Applications: Minimization Problems

Mathematics

273Introduction to Systems of Linear Equations
274Solving Systems by Graphing: Basic Technique
275Types of Solutions: One, None, or Infinitely Many
276Graphing Systems with Parallel and Coincident Lines
277Introduction to the Substitution Method
278Substitution When One Equation is Already Solved
279Substitution Requiring Solving for a Variable First
280Identifying No Solution or Infinite Solutions via Substitution
281Comparing Graphing and Substitution Methods
282Application Problems Using Systems and Substitution
283Introduction to the Elimination Method
284Eliminating a Variable by Adding Equations
285Eliminating a Variable by Subtracting Equations
286Multiplying One Equation to Enable Elimination
287Multiplying Both Equations to Enable Elimination
288Choosing the Easier Variable to Eliminate
289Elimination with Fractions and Decimals
290Special Cases: No Solution and Infinite Solutions
291Word Problems Solved by Elimination
292Introduction to Three-Variable Systems
293Visualizing Three-Variable Systems
294Solving Three-Variable Systems by Elimination
295Choosing Strategic Pairs for Elimination
296Back-Substitution in Three Variables
297Inconsistent Three-Variable Systems
298Dependent Three-Variable Systems
299Applications of Three-Variable Systems
300Graphing Linear Inequalities in Two Variables
301Systems of Linear Inequalities
302Vertices of the Feasible Region
303Bounded vs Unbounded Feasible Regions
304Introduction to Linear Programming
305The Objective Function
306The Corner Point Theorem
307Solving Linear Programming Problems Graphically
308Applications: Maximization Problems
309Applications: Minimization Problems

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Lesson 296 of 3,121·8. Systems of Linear Equations and InequalitiesPro lesson

Back-Substitution in Three Variables

After finding one variable, substitute back through reduced equations to find remaining variables.

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