Systems of Linear Equations Word Problems

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What is a system of linear equations?

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A system of linear equations is a set of two or more linear equations with the same variables. The solution to the system is the point(s) where the equations intersect on a graph.

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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 express the total or constraints as equations.

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What does it mean if two equations in a system are 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 if two equations in a system are 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 if two equations in a system are 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 determine the number of solutions in a system of linear equations?

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By analyzing the slopes and y-intercepts of the lines represented by the equations: if they intersect, there is one solution; if they are parallel, there are no solutions; if they are the same line, there are infinitely many solutions.

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What is the substitution method for 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 for 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 do you interpret the solution of a system of equations in a real-world context?

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The solution represents the values of the variables that satisfy all equations in the system, often corresponding to quantities or amounts in a real-world scenario.

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What is a linear equation?

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