system of equation word problem

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

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What are the methods to solve a system of equations?

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The main methods to solve a system of equations are: 1) Graphing, 2) Substitution, 3) Elimination, and 4) Matrix methods.

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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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What does it mean for a system of equations to be consistent?

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A consistent system of equations has at least one solution. It can be either a unique solution or infinitely many solutions.

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What does it mean for a system of equations to be inconsistent?

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An inconsistent system of equations has no solutions, meaning the equations represent parallel lines that never intersect.

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What is a unique solution in the context of systems of equations?

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A unique solution occurs when there is exactly one set of values for the variables that satisfies all equations in the system.

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

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A system has infinitely many solutions if the equations are dependent, meaning they represent the same line in a graph.

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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 involves plotting each equation on a coordinate plane and identifying the points of intersection.

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

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Coefficients are the numerical factors in front of the variables in an equation. They determine the slope and position of the lines when graphed.