Systems of linear equations

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What are systems of linear equations?

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

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How many solutions can a system of linear equations have?

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No solution, One solution, or Infinitely many solutions.

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What does the graph of a system with no solution look like?

Back

Parallel lines.

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What does the graph of a system with infinitely many solutions look like?

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Coinciding lines (the same line).

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What is a linear equation?

Back

An equation that makes a straight line when graphed, typically in the form y = mx + b.

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What is the substitution method in solving systems of equations?

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

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

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The system of equations has one unique solution.

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What is the graphical representation of a system of equations?

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The intersection points of the lines representing the equations.

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

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If the lines are parallel and never intersect.