Solving 3-variable systems REVIEW

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution to the system is the set of values that satisfy all equations simultaneously.

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What are the two main methods for solving systems of equations?

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The two main methods for solving systems of equations are substitution and elimination.

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How does the substitution method work?

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In the substitution method, one equation is solved for one variable, and then that expression is substituted into the other equation(s) to solve for the remaining variables.

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How does the elimination method work?

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In the elimination method, equations are manipulated (by addition or subtraction) to eliminate one variable, allowing the remaining variables to be solved.

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What does it mean for a system of equations to be consistent?

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A consistent system of equations has at least one solution, meaning the equations intersect at one or more points.

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What does it mean for a system of equations to be inconsistent?

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An inconsistent system of equations has no solution, meaning the equations represent parallel lines that never intersect.

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What is a dependent system of equations?

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A dependent system of equations has infinitely many solutions, meaning the equations represent the same line.

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What is the significance of the solution (3, 3, -4) in a 3-variable system?

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The solution (3, 3, -4) indicates the values of the three variables that satisfy all equations in the system.

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How can word problems be translated into systems of equations?

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Word problems can be translated into systems of equations by identifying the variables, writing equations based on the relationships described, and ensuring all conditions are represented.

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What is the first step in solving a word problem involving a system of equations?

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The first step is to define the variables that represent the unknown quantities in the problem.