Solving Systems of Equations (All Methods)

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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 that are solved together.

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What does it mean to solve a system of equations?

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Finding the values of the variables that satisfy all equations in the system simultaneously.

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What is the elimination method?

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A technique for solving systems of equations by adding or subtracting equations to eliminate one variable.

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What is the substitution method?

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A technique for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

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What is the graphing method?

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A technique for solving systems of equations by graphing the equations on the same coordinate plane and identifying the point of intersection.

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What is the solution to the system of equations: -x + y = -13 and -8x - 4y = -8?

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(5, -8)

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What is the solution to the system of equations: y = 3x - 8 and y = 4 - x?

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(3, 1)

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What is the solution to the system of equations: y = x + 2 and y = -x?

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(-1, 1)

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True or False: The solution to a system of equations is the same regardless of the method used to solve it.

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True; using any method will result in the correct solution.

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What is the first step in the elimination method?

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Align the equations so that like terms are in the same column.