Algebra Topic 4 Systems of Equations & Inequalities

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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 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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What is the slope-intercept form of a linear equation?

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How do you convert an equation to slope-intercept form?

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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, or not equal to the other.

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What does it mean for a solution to a system of inequalities?

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The solution to a system of inequalities is the region on a graph where all the inequalities overlap.

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

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What does the term 'feasible region' refer to in linear programming?

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The feasible region is the area on a graph that satisfies all constraints of a system of inequalities.

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How can 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 point's coordinates into each equation. If it satisfies all equations, it is a solution.