Systems 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 represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

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What does it mean if two equations in a system are independent?

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Independent equations have different slopes and intersect at exactly one point, meaning there is one unique solution.

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What does it mean if two equations in a system are dependent?

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Dependent equations represent the same line, meaning there are infinitely many solutions.

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What does it mean if two equations in a system are inconsistent?

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Inconsistent equations have no solutions because they represent parallel lines that never intersect.

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How do you solve a system of equations using substitution?

Back

Solve one equation for one variable, then substitute that expression into the other equation to find the value of the second variable.

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How do you solve a system of equations using elimination?

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Add or subtract the equations to eliminate one variable, making it easier to solve for the remaining variable.

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What is the significance of the solution to a system of equations in a word problem?

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The solution represents the values of the variables that satisfy all equations, providing answers to the original problem.

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How can 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 a linear equation?

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A linear equation is an equation that forms a straight line when graphed, typically in the form y = mx + b.