Algebra 2 Section 3.2 Solving Systems Algebraically

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What is a system of equations?

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A set of two or more equations with the same variables.

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What does it mean to solve a system of equations algebraically?

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Finding the values of the variables that satisfy all equations in the system using algebraic methods.

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What is the substitution method in solving systems of equations?

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A method where one equation is solved for one variable, and that expression is substituted into the other equation.

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What is the elimination method in solving systems of equations?

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A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

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What is a consistent system of equations?

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A system that has at least one solution.

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What is an inconsistent system of equations?

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A system that has no solutions.

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What is a dependent system of equations?

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A system that has infinitely many solutions, where the equations represent the same line.

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How do you check the solution of a system of equations?

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Substitute the solution back into the original equations to verify if both equations are satisfied.

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What is the graphical method of solving systems of equations?

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Plotting the equations on a graph and identifying the point(s) where they intersect.

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What does it mean for two lines to be parallel in the context of systems of equations?

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They have the same slope but different y-intercepts, indicating no solutions exist.