system 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 graphically?

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To solve graphically, plot each equation on the same graph and identify the point(s) where they intersect.

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What does it mean to have no solution in a system of equations?

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No solution means the lines represented by the equations are parallel and never intersect.

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What does it mean to have infinitely many solutions in a system of equations?

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Infinitely many solutions occur when the equations represent the same line, meaning every point on the line is a solution.

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What is the substitution method for solving systems of equations?

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The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

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What is the elimination method for 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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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 a real-world example of a system of equations?

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A real-world example is determining the number of two types of items sold, like cones and cups, based on total sales and total items.

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What is the importance of checking your solution in a system of equations?

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Checking ensures that the solution satisfies all equations in the system, confirming its validity.

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How do you interpret the solution of a system of equations in a word problem?

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The solution represents the values of the variables that satisfy the conditions of the problem, often answering a specific question.