Systems of Equations - Word Problems

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

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Identify the variables, translate the relationships and conditions described in the problem into equations, and ensure the equations represent the same scenario.

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What does it mean for two equations to be equivalent?

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Two equations are equivalent if they have the same solution set, meaning they represent the same line or relationship in a graph.

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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 to find the values of both variables.

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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 can you determine if a system of equations has no solution?

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A system has no solution if the equations represent parallel lines, which means they never intersect.

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What does it mean for a system of equations to have 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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In the context of word problems, what is a variable?

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A variable is a symbol used to represent an unknown quantity in equations, often corresponding to real-world quantities like price, quantity, or distance.

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How do you interpret the solution of a system of equations in a word problem?

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The solution represents the values of the variables that satisfy all conditions of the problem, often corresponding to quantities like price or number of items.

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What is a linear equation?

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A linear equation is an equation that forms a straight line when graphed, typically in the form y = mx + b, where m is the slope and b is the y-intercept.