Systems of Linear Equations Practce

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What is a system of linear equations?

Back

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

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What does it mean to solve a system of linear equations?

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

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What is the graphical representation of a linear equation?

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A straight line on a coordinate plane, where each point on the line represents a solution to the equation.

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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 does the x-coordinate represent in a word problem involving linear equations?

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Typically represents the independent variable, such as time or quantity, depending on the context of the problem.

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What does the y-coordinate represent in a word problem involving linear equations?

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Typically represents the dependent variable, such as cost or distance, depending on the context of the problem.

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

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

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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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What is the significance of the point of intersection in a system of linear equations?

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It represents the solution to the system, indicating the values of the variables that satisfy all equations.

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What does it mean if two lines are parallel in a system of linear equations?

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The system has no solution, as the lines never intersect.