System Of Equation 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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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 satisfy all equations in the system simultaneously.

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What are the two main methods for solving systems of equations?

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The two main methods are the substitution method and the elimination method.

Front

What is the substitution method?

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

Front

What is the elimination method?

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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 ensure they represent the same situation.

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What is a variable in the context of a system of equations?

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A variable is a symbol used to represent an unknown quantity in an equation.

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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 do 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.