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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 simultaneously.

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

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

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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 is the graphical interpretation of a system of equations?

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The graphical interpretation involves plotting each equation on a coordinate plane. The point(s) where the lines intersect represent the solution(s) to the system.

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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 substituting that expression into the other equation.

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

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Coefficients represent the relationship between the variables in the equations. They determine the slope and position of the lines when graphed.

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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 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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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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How can you check the solution of a system of equations?

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You can check the solution by substituting the values back into the original equations to see if they hold true.

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

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Constants in a system of equations represent fixed values that affect the position of the lines on a graph.