System of Equations Review

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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What are the methods to solve systems of equations?

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Common methods include graphing, substitution, elimination, and matrix methods.

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What does it mean if a system of equations has no solution?

Back

It means that the lines represented by the equations are parallel and never intersect.

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What does it mean if a system of equations has infinitely many solutions?

Back

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

Front

How do you solve a system of equations using the substitution method?

Back

To solve using substitution, solve one equation for one variable and substitute that expression into the other equation.

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How do you solve a system of equations using the elimination method?

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To solve using elimination, manipulate the equations to eliminate one variable, allowing you to solve for the other.

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What is the graphical representation of a system of equations?

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The graphical representation consists of the lines of the equations plotted on a coordinate plane, with the solution being the intersection point(s).

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

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Coefficients determine the slope and position of the lines represented by the equations.

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What is the difference between consistent and inconsistent systems?

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A consistent system has at least one solution, while an inconsistent system has no solutions.

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What is the role of the determinant in solving systems of equations?

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The determinant helps determine whether a system of linear equations has a unique solution, no solution, or infinitely many solutions.