73 WarmUp: Graphing SOE/Ineqs

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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 on a graph.

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What does it mean for a point to be a solution to a system of equations?

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A point is a solution to a system of equations if it satisfies all equations in the system, meaning it makes all equations true when substituted.

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How do you graph a linear equation?

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To graph a linear equation, convert it to slope-intercept form (y = mx + b), identify the slope (m) and y-intercept (b), and plot the line using these points.

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What is the difference between a solid line and a dashed line in graphing inequalities?

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A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

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What does shading represent in a graph of inequalities?

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Shading represents the set of all solutions that satisfy the inequality. The shaded region includes all points that make the inequality true.

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How do you determine which region to shade when graphing a system of inequalities?

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To determine which region to shade, test a point not on the line (often (0,0)) in the inequality. If the inequality holds true, shade the region that includes that point.

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What is the solution to the system of equations represented graphically?

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The solution to the system of equations is the point(s) where the graphs of the equations intersect.

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What is an inequality?

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An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, greater than or equal to, or less than or equal to the other.

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