Review Systems of Linear Equations and Inequalities

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What is a system of linear equations?

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A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the graphs of the equations intersect.

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What does it mean for a system of equations to have no solution?

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A system of equations has no solution when the lines represented by the equations are parallel and never intersect.

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

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To determine if a point is a solution, substitute the x and y values of the point into each equation. If the point satisfies all equations, it is a solution.

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What is the difference between a linear equation and a linear inequality?

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A linear equation represents a straight line, while a linear inequality represents a region of the graph where the inequality holds true, often shaded.

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

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The slope of a line represents the rate of change of y with respect to x, indicating how steep the line is.

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What does it mean for a system of inequalities to be represented graphically?

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Graphically, a system of inequalities is represented by shading the regions of the graph that satisfy all inequalities.

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How can you tell if two lines are parallel from their equations?

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Two lines are parallel if they have the same slope (m) but different y-intercepts (b) in their equations.