Systems of Equations And Inequalities

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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 graphs of the equations intersect.

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 be consistent?

Back

A consistent system of equations has at least one solution, meaning the graphs of the equations intersect at one or more points.

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CCSS.8.EE.C.8B

Front

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

Back

An inconsistent system of equations has no solutions, meaning the graphs of the equations do not intersect.

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CCSS.8.EE.C.8B

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What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on a coordinate plane.

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How do you solve a system of equations using substitution?

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To solve by substitution, solve one equation for one variable, then substitute that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you solve a system of equations using elimination?

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To solve by elimination, add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

Tags

CCSS.6.EE.B.8

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What does it mean for a solution to satisfy an inequality?

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A solution satisfies an inequality if it makes the inequality true when substituted into the expression.

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CCSS.6.EE.B.5

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

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A linear equation has a degree of 1 and graphs as a straight line, while a quadratic equation has a degree of 2 and graphs as a parabola.

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What is the vertex of a parabola?

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The vertex of a parabola is the highest or lowest point on the graph, depending on its orientation.