Unit 5 Review: Systems of Equations

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 for a system of equations to have one solution?

Back

It means that the equations intersect at exactly one point on the graph.

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What does it mean for a system of equations to have no solution?

Back

It means that the equations represent parallel lines that never intersect.

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What does it mean for a system of equations to have infinitely many solutions?

Back

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

Front

How do you represent a system of equations graphically?

Back

By plotting each equation on the same coordinate plane and finding the intersection points.

Front

What is the standard form of a linear equation?

Back

Ax + By = C, where A, B, and C are constants.

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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 that expression is substituted into the other equation.

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What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

What is an ordered pair?

Back

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

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the x and y values of the point into each equation to see if they hold true.