Systems of Equations and Inequalities Review

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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 if a system of equations has no solution?

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If a system of equations has no solution, the graphs of the equations are parallel lines, meaning they never intersect.

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What is the graphical representation of a system of equations with infinitely many solutions?

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The graphical representation is when the equations are the same line, meaning they overlap completely.

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How do you determine if a point is a solution to a system of equations?

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Substitute the point's coordinates into each equation. If the equations are satisfied, the point is a solution.

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What is the difference between a system of equations and a system of inequalities?

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A system of equations consists of equations that can be solved for exact points, while a system of inequalities includes inequalities that define a range of possible solutions.

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What does the solution to a system of inequalities represent graphically?

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The solution represents a shaded region on a graph where all the points satisfy the inequalities.

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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.

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What is a linear equation?

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What does the slope of a line represent in a linear equation?

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The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates the steepness and direction of the line.