Systems of Equations & Inequalities

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What is a system of equations?

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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?

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It means that the graphs of the equations intersect at exactly one point.

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

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It means that the graphs of the equations are parallel and never intersect.

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

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It means that the equations represent the same line, so they intersect at every point on that line.

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How do you graph a system of inequalities?

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Graph each inequality on the same coordinate plane and identify the region where the solutions overlap.

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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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How can you determine if two equations are independent?

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If they have different slopes and intersect at one point, they are independent.