Solving a System 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?

Back

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

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What is the graphical method of solving a system of equations?

Back

Plotting the equations on a graph and identifying the point(s) where they intersect.

Front

What is an ordered pair in the context of a system of equations?

Back

A pair of numbers (x, y) that represents a point on the coordinate plane.

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

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The lines representing the equations are parallel and never intersect.

Front

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

Back

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

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

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By using methods such as substitution, elimination, or matrix operations.

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What is the substitution method?

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A method for solving a system of equations by solving one equation for one variable and substituting that expression into the other equation.

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What is the elimination method?

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A method for solving a system of equations by adding or subtracting equations to eliminate one variable.

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What is a consistent system of equations?

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A system that has at least one solution.