Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

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What does it mean for a point to be a solution to a system of equations?

Back

It means that the point satisfies all equations in the system.

Front

What are the three main methods to solve systems of linear equations?

Back

Graphing, Substitution, and Elimination.

Front

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

Back

Substitute the point's coordinates into each equation and check if they hold true.

Front

What is the elimination method?

Back

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

Front

What is the substitution method?

Back

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

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What does it mean if two lines intersect at a point on a graph?

Back

It means that the system of equations has one unique solution.

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What does it mean if two lines are parallel on a graph?

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It means that the system of equations has no solution.

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What does it mean if two lines coincide on a graph?

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It means that the system of equations has infinitely many solutions.

Front

How can you represent a real-world situation with a system of equations?

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By defining variables for the quantities involved and writing equations based on relationships between those quantities.