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 is the point(s) where the equations intersect.

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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 to solve a system of equations?

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To find the values of the variables that satisfy all equations in the system simultaneously.

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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 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 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.

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What does it mean for two equations to be dependent?

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Dependent equations are equations that represent the same line, meaning they have infinitely many solutions.

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What does it mean for two equations to be independent?

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Independent equations are equations that represent different lines, meaning they have exactly one solution.

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What does it mean for two equations to be inconsistent?

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Inconsistent equations are equations that represent parallel lines, meaning they have no solutions.

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

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Substitute the solution back into the original equations to see if it satisfies all equations.