Systems of Equations Word Problems

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What is a system of equations?

Back

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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To solve by substitution, solve one equation for one variable, then substitute 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 other.

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What does it mean for a system of equations to be consistent?

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A consistent system has at least one solution, meaning the equations intersect at one or more points.

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What does it mean for a system of equations to be inconsistent?

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An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

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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.

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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 equal to each other.

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What is the first step in solving a word problem involving a system of equations?

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Read the problem carefully, identify the variables, and determine what is being asked.

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Example of a word problem: If 3x + 2y = 12 and 4x - y = 5, what are x and y?

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x = 2, y = 3.

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How do you check your solution for a system of equations?

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Substitute the values of the variables back into the original equations to see if they hold true.