Systems of Equations and Inequalities

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What is a system of equations?

Back

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 infinitely many solutions?

Back

It means that the equations represent the same line, and any point on that line is a solution.

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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 an inconsistent system of equations?

Back

A system that has no solutions, typically because the lines are parallel.

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What is a consistent system of equations?

Back

A system that has at least one solution, which can be either one solution or infinitely many.

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How do you determine if two equations represent the same line?

Back

If the equations can be transformed into each other through multiplication or addition of constants.

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What is the graphical representation of a system of equations?

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The points where the graphs of the equations intersect represent the solutions to the system.

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What does it mean for a system of equations to have a unique solution?

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It means that the lines intersect at exactly one point.

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How can you represent a system of equations algebraically?

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Using equations in the form ax + by = c, where a, b, and c are constants.

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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, making it easier to solve for the other.