Solving Systems of Linear Equations

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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 two lines to intersect on a graph?

Back

It means they have a common solution, which is the point where they meet.

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What is the solution to a system of equations?

Back

An ordered pair (x, y) that satisfies all equations in the system.

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What is substitution in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into another equation.

Front

How do you check if an ordered pair is a solution to a system of equations?

Back

Substitute the values of the ordered pair into both equations to see if they hold true.

Front

What is the graphical representation of a system of linear equations?

Back

It is represented by lines on a coordinate plane.

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What does it mean if two lines are parallel in a system of equations?

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They have no solutions because they never intersect.

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What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable.

Front

What is the first step in solving a system of equations by substitution?

Back

Solve one of the equations for one variable in terms of the other.

Front

What is an ordered pair?

Back

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