Solving Systems of Equations Flashcard

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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

Back

Finding the point(s) where the graphs of the equations intersect, which represents the solution(s) to the system.

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What is the elimination method in solving systems of equations?

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A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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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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How do you determine if a system of equations has no solution?

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If the equations represent parallel lines, they will never intersect, indicating no solution.

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How do you determine if a system of equations has infinitely many solutions?

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If the equations represent the same line, every point on the line is a solution, indicating infinitely many solutions.

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What is the coordinate pair solution of a system of equations?

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The values of the variables that satisfy all equations in the system, expressed as (x,y).

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

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A system is consistent if it has at least one solution.

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

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A system is inconsistent if it has no solutions.

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How can you check your solution to a system of equations?

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By substituting the values back into the original equations to see if they hold true.