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 find the values of the variables.

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How does the elimination method work?

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In the elimination method, equations are manipulated to eliminate one variable, allowing the remaining variable to be solved easily.

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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 solutions, 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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How can you represent a word problem as a system of equations?

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To represent a word problem as a system of equations, identify the variables, translate the relationships and conditions into equations, and ensure all equations are aligned with the problem's context.

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What is the importance of checking your solution in a system of equations?

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Checking your solution ensures that the values satisfy all original equations, confirming that the solution is correct.

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What is the graphical interpretation of a system of equations?

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The graphical interpretation involves plotting the equations on a coordinate plane; the points of intersection represent the solutions to the system.