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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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 up as a system.

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

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The first step is to define the variables that represent the unknown quantities in the problem.

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How do you check the solution of a system of equations?

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Substitute the solution back into the original equations to verify that both equations are satisfied.

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What is the importance of units in word problems?

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Units help ensure that the quantities being compared or calculated are consistent, which is crucial for accurate solutions.