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 that the lines represented by the equations are parallel and never intersect.

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How do you represent a word problem as a system of equations?

Back

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

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

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What is the graphical method for solving systems of equations?

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The graphical method involves graphing both equations on the same coordinate plane and identifying the point of intersection.

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What does it mean for two equations to be dependent?

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Dependent equations are equations that represent the same line, meaning they have infinitely many solutions.

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What does it mean for two equations to be independent?

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Independent equations are equations that represent different lines, meaning they have exactly one solution.

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How do you determine the number of solutions in a system of equations?

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By analyzing the slopes and y-intercepts of the lines represented by the equations: parallel lines (no solution), same line (infinitely many solutions), or intersecting lines (one solution).