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 set of values that satisfy all equations in the system.

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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 for two variables to be dependent?

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Two variables are dependent if the value of one variable can be expressed as a function of the other, meaning they are related.

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What does it mean for two variables to be independent?

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Two variables are independent if the value of one variable does not affect the value of the other, meaning they are not related.

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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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How do you solve a system of equations using elimination?

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1. Align the equations. 2. Multiply equations if necessary to align coefficients. 3. Add or subtract equations to eliminate one variable. 4. Solve for the remaining variable.

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What is the significance of the solution to a system of equations?

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The solution represents the point(s) where the equations intersect, indicating the values of the variables that satisfy all equations.

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What is a word problem?

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A word problem is a mathematical problem presented in a narrative form, requiring interpretation and translation into mathematical expressions.

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

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Substitute the solution values back into the original equations to verify that both equations hold true.

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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, where m is the slope and b is the y-intercept.