Solving 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 solve a system of equations using substitution?

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1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

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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 other variable.

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What does it mean to graph a system of equations?

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Graphing a system of equations involves plotting each equation on the same coordinate plane to visually find the point(s) of intersection.

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What is a word problem in mathematics?

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A word problem is a mathematical problem presented in a narrative form, requiring translation into equations to solve.

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How can 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 set them up as a system.

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What is the importance of checking your solution in a system of equations?

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Checking your solution ensures that the values satisfy all equations in the system, confirming that the solution is correct.

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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 has the form y = mx + b, where m is the slope and b is the y-intercept.

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What is the meaning of 'cost' in a word problem context?

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Cost refers to the total amount of money spent on items or services, often represented in equations to find unknown values.

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How do you set up an inequality from a word problem?

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Identify the constraints or limits in the problem, then express them using inequality symbols (>, <, ≥, ≤) based on the context.