Test Solve Systems of Equations Using Elimin., Subst., Graph

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?

Back

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

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What is the elimination method?

Back

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?

Back

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

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The lines represented by 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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The equations represent the same line, meaning every point on the line is a solution.

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How do you graph a system of equations?

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Plot each equation on the same coordinate plane and identify the point(s) where they intersect.

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What is the first step in the elimination method?

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

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How can you manipulate equations to use the elimination method?

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You can multiply one or both equations by a constant to create coefficients that will cancel out when added or subtracted.

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What is the solution to the system: 2x + 3y = 6 and x - y = 1?

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(3, 0) - found by using either elimination or substitution.