Solving Systems (All Methods)

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What is a system of equations?

Back

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 by graphing?

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It means to find the point(s) where the graphs of the equations intersect.

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What is the elimination method in solving systems of equations?

Back

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?

Back

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

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What does it mean if a system of equations has no solution?

Back

It means the lines representing the equations are parallel and never intersect.

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What does it mean if a system of equations has infinitely many solutions?

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It means the equations represent the same line, so every point on the line is a solution.

Front

How do you determine the solution of a system of equations graphically?

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By identifying the point(s) where the graphs of the equations intersect.

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What is the first step in solving a system of equations by elimination?

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Align the equations so that corresponding variables and constants are in the same columns.

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What is the purpose of multiplying an equation in the elimination method?

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To create coefficients that will allow one variable to be eliminated when the equations are added or subtracted.

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What is a consistent system of equations?

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A system that has at least one solution.