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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, write equations based on the relationships described in the problem, and ensure the equations reflect the conditions given.

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What does it mean to solve a system of equations?

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To solve a system of equations means to find the values of the variables that make all equations true simultaneously.

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What is the substitution method in solving systems of equations?

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The substitution method involves solving one equation for one variable and then substituting 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 remaining variable.

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How can you check if your solution to a system of equations is correct?

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Substitute the values of the variables back into the original equations to see if they satisfy all equations.

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What is the significance of the coefficients in a system of equations?

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Coefficients represent the relationship between the variables in the equations. They determine how changes in one variable affect the other.

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What does it mean if a system of equations has no solution?

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A system has no solution if the equations represent parallel lines that never intersect, meaning there are no values that satisfy both equations.

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What does it mean if a system of equations has infinitely many solutions?

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A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

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How do you write an equation for a total cost problem?

Back

Identify the cost per item and the number of items, then write an equation that represents the total cost as the sum of the costs of each item.