Systems of Equations - Elimination + Substitution

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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 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 the elimination method and the substitution method.

Front

Explain the elimination method for solving systems of equations.

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

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Explain the substitution method for solving systems of equations.

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The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

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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 the graphical representation of a system of equations?

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The graphical representation of a system of equations is the intersection of the lines or curves represented by the equations on a coordinate plane.

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

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The solution of a system of equations graphically is found at the point(s) where the graphs of the equations intersect.

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What is the first step in using the elimination method?

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The first step in using the elimination method is to align the equations and manipulate them to create coefficients that will allow one variable to be eliminated.

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What is the first step in using the substitution method?

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The first step in using the substitution method is to solve one of the equations for one variable in terms of the other variable.