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 represent a word problem as a system of equations?

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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 the variable 'x' typically represent in a system of equations?

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In a system of equations, 'x' usually represents one of the unknown quantities that you are trying to solve for.

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What does the variable 'y' typically represent in a system of equations?

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In a system of equations, 'y' usually represents another unknown quantity that is related to 'x'.

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

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The first step is to write the equations in a standard form, if they are not already.

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What is substitution in the context of solving systems of equations?

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Substitution is a method where you solve one equation for one variable and then substitute that expression into the other equation.

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What is elimination in the context of solving systems of equations?

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Elimination is a method where you add or subtract equations to eliminate one variable, making it easier to solve for 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.

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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 they intersect at every point on that line.

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

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You can check by substituting the solution back into the original equations to see if they hold true.