Choosing the Best Method (Systems)

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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 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 variable.

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When is it best to use the Substitution Method?

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The Substitution Method is best used when one equation is easily solvable for one variable.

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When is it best to use the Elimination Method?

Back

The Elimination Method is best used when the coefficients of one variable are the same or can be made the same.

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What does it mean if a system of equations has one solution?

Back

It means the lines intersect at exactly one point, representing a unique solution.

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

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It means the lines are parallel and never intersect, indicating that there is no point that satisfies both equations.

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

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It means the lines coincide, or are the same line, indicating that there are countless points that satisfy both equations.

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How can you determine if a system of equations has one solution, no solution, or infinitely many solutions?

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By analyzing the slopes and y-intercepts of the equations: if slopes are different, one solution; if slopes are the same and intercepts are different, no solution; if slopes and intercepts are the same, infinitely many solutions.

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What is the graphical representation of a system of equations?

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The graphical representation consists of lines on a coordinate plane, where their intersections represent the solutions.

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What is the importance of the slope in a system of equations?

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The slope indicates the steepness of the line and helps determine the relationship between the two equations.