Systems of Equations & Inequalities

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What is a system of equations?

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A set of two or more equations with the same variables that are solved together.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean for a system of equations to have one solution?

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It means that the equations intersect at exactly one point on the graph.

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CCSS.8.EE.C.8A

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

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It means that the equations represent parallel lines that never intersect.

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CCSS.8.EE.C.8A

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What does it mean for a system of equations to have infinite solutions?

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It means that the equations represent the same line, so every point on the line is a solution.

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CCSS.8.EE.C.8B

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What is an inequality?

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An inequality is a mathematical statement that compares two expressions using symbols like <, >, ≤, or ≥.

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How do you graph a linear inequality?

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Graph the corresponding linear equation as a solid line (if ≤ or ≥) or dashed line (if < or >) and shade the appropriate region.

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CCSS.HSA.REI.D.12

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What is the feasible region in a system of inequalities?

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The feasible region is the area on the graph where all the inequalities overlap, representing all possible solutions.

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CCSS.HSA.REI.D.12

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What is substitution in solving systems of equations?

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Substitution is a method where you solve one equation for one variable and then substitute that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is elimination in solving systems of equations?

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Elimination is a method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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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 if it satisfies all equations in the system when substituted into them.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6