Systems of equations

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What is a system of equations?

Back

A set of two or more equations with the same variables.

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What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

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What is the graphical representation of a system of equations?

Back

The intersection points of the lines representing the equations.

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What is a consistent system of equations?

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A system that has at least one solution.

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What is an inconsistent system of equations?

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A system that has no solutions.

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What is a dependent system of equations?

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A system that has infinitely many solutions, where the equations represent the same line.

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How do you determine the solution of a system of equations graphically?

Back

By finding the point(s) where the graphs of the equations intersect.

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What is 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 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 is the importance of the coefficients in a system of equations?

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They determine the slope and position of the lines in the graphical representation.