5.4 Alg 1A 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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What does it mean to solve a system of equations?

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To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

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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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What is the graphing method for solving systems of equations?

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The graphing method involves graphing each equation on the same set of axes and identifying the point(s) where they intersect.

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What is a linear equation?

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A linear equation is an equation that makes a straight line when graphed. It can be written 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 equivalent?

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Two equations are equivalent if they have the same solution set, meaning they intersect at the same point(s) 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 ensure the equations represent the same situation.

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What is the significance of the intersection point in a system of equations?

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The intersection point represents the solution to the system, indicating the values of the variables that satisfy all equations.

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What is a dependent system of equations?

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A dependent system has infinitely many solutions, meaning the equations represent the same line.