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

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A system of equations has no solution if the equations represent parallel lines that never intersect.

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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 other variable.

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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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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 they are dependent.

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What is the graphical interpretation of a system of equations?

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The graphical interpretation involves plotting the equations on a coordinate plane; the point(s) where the lines intersect represent the solution(s) of the system.

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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 adding or subtracting them will eliminate one variable.

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What does it mean for two equations to be independent?

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Two equations are independent if they have exactly one solution, meaning their graphs intersect at exactly one point.

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

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The coefficients determine the slope and position of the lines represented by the equations, affecting the number of solutions.

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How can you check your solution to a system of equations?

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