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 a system of equations to have a unique solution?

Back

It means the lines intersect at exactly one point.

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

Back

It means the lines are parallel and never intersect.

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

Back

It means the lines overlap each other.

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How can you determine if a system of equations has no solution?

Back

If the equations represent parallel lines.

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What is an ordered pair in the context of systems of equations?

Back

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

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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 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?

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A method where you add or subtract equations to eliminate one variable.

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What does it mean to eliminate a variable?

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To remove one variable from the equations to simplify the system.