Systems of Equations Test

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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 to the system is the set of values that satisfy all equations simultaneously.

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What does it mean to solve a system of equations by elimination?

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Solving by elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

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What is the elimination method?

Back

The elimination method is a technique for solving systems of equations by combining the equations to eliminate one variable, allowing for the solution of the other variable.

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

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A system has no solution if the equations represent parallel lines that never intersect, indicating that there are no values for the variables that satisfy all equations.

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What is the graphical representation of a system of equations?

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The graphical representation of a system of equations is the intersection point(s) of the lines represented by the equations on a coordinate plane.

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How do you determine if a system of equations has infinitely many solutions?

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A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

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What is the first step in solving a system of equations using the elimination method?

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The first step is to align the equations and manipulate them (if necessary) so that the coefficients of one variable are opposites.

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What is the solution to the system of equations 6x - y = 2 and -3x - 6y = 12?

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The solution is (0, -2).

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What does it mean for two equations to be dependent?

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Two equations are dependent if they represent the same line, resulting in infinitely many solutions.

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What is the solution to the system of equations 3x + y = -5 and 6x + 2y = 10?

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The system has no solution, indicating the lines are parallel.