Systems of Equations Word Problems

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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 point(s) where the equations intersect.

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

Back

It means the lines represented by the equations are parallel and never intersect.

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

Back

It means the equations represent the same line, so every point on the line is a solution.

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What is the elimination method?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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What is the substitution method?

Back

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 graphing method?

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The graphing method involves graphing each equation on the same coordinate plane to find the point(s) of intersection.

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What is the meaning of the variables in a system of equations?

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Variables represent unknown quantities that we are trying to solve for in the equations.

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

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You can substitute the solution back into the original equations to see if both equations are satisfied.

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What is a word problem in the context of systems of equations?

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A word problem is a real-life scenario that can be modeled using a system of equations to find unknown values.

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How do you translate a word problem into a system of equations?

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Identify the variables, write equations based on the relationships described in the problem, and ensure they represent the same situation.