Systems of Equations review for Chapter test

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations in the system.

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How do you represent a word problem as a system of equations?

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Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

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What does it mean if a system of equations has one solution?

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It means the lines represented by the equations intersect at exactly one point, indicating a unique solution for the variables.

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

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It means the lines represented by the equations are parallel and never intersect, indicating that there are no values that satisfy both equations.

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

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It means the lines represented by the equations coincide, indicating that there are an infinite number of points that satisfy both equations.

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How can you determine if a system of equations is consistent or inconsistent?

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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 substitution method in solving systems of equations?

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The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

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What is the elimination method in solving systems of equations?

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

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How do you graph a system of equations?

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Graph each equation on the same coordinate plane and identify the point(s) of intersection to find the solution(s).

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What is the importance of checking your solution in a system of equations?

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Checking the solution ensures that the values satisfy all equations in the system, confirming the solution's validity.