Systems of Equations and Inequalities Quick Check

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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 is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the inequalities overlap on a graph.

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How do you solve a system of inequalities by graphing?

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1. Graph each inequality on the same coordinate plane. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the appropriate region for each inequality. 4. The solution is where the shaded regions overlap.

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What does the solution of a system of equations represent?

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The solution of a system of equations represents the point(s) where the graphs of the equations intersect, indicating the values of the variables that satisfy all equations.

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What does it mean if two lines are parallel in a system of equations?

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If two lines are parallel, it means they have no points of intersection, indicating that the system has no solution.

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What does it mean if two lines coincide in a system of equations?

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If two lines coincide, it means they are the same line, indicating that the system has infinitely many solutions.

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

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You can determine the number of solutions by analyzing the slopes and y-intercepts of the lines: 1. Different slopes = one solution. 2. Same slope, different intercepts = no solution. 3. Same slope, same intercept = infinitely many solutions.

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What is the graphical representation of the inequality y < 2x - 4?

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The graphical representation is a dashed line for y = 2x - 4, with the area below the line shaded.

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What is the significance of the boundary line in a system of inequalities?

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The boundary line separates the coordinate plane into two regions, indicating where the inequality holds true (shaded region) and where it does not (unshaded region).

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How do you write inequalities from a word problem?

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Identify the variables, determine the constraints, and express them as inequalities based on the relationships described in the problem.