Writing Systems of Equations

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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 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?

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Identify the variables, translate the relationships and conditions into equations, and ensure the equations represent the same scenario.

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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 we 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 purpose of solving a system of equations?

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The purpose is 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 other.

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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 hold true.

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

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It means that the equations represent parallel lines that never intersect, indicating that there are no values that satisfy all equations.

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

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It means that the equations represent the same line, and any point on that line is a solution.