System of Equations and 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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean for an ordered pair to be a solution to a system of equations?

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An ordered pair is a solution to a system of equations if it satisfies all equations in the system, meaning when substituted into the equations, they hold true.

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How can you determine if an ordered pair is a solution to a system of equations?

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To determine if an ordered pair is a solution, substitute the values of the ordered pair into each equation of the system. If all equations are satisfied, it is a solution.

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What is the graphical representation of a system of equations?

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The graphical representation of a system of equations consists of the lines or curves of each equation plotted on a coordinate plane. The intersection points represent the solutions.

Tags

CCSS.HSA.REI.C.7

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What is an inequality in the context of systems?

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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. In systems, inequalities can define regions on a graph.

Tags

CCSS.HSA.REI.D.12

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What is the difference between a solution to an equation and a solution to an inequality?

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A solution to an equation is a specific point that satisfies the equation, while a solution to an inequality represents a range of values that satisfy the inequality.

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What does it mean for a point to be part of the solution set of a system of inequalities?

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A point is part of the solution set of a system of inequalities if it lies in the region defined by the inequalities on a graph.

Tags

CCSS.HSA.REI.D.12

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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 to find the value of the second variable.

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, manipulate the equations to eliminate one variable by adding or subtracting the equations, then solve for the remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the significance of the intersection point in a system of equations?

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The intersection point represents the unique solution to the system of equations, where all equations are satisfied simultaneously.

Tags

CCSS.8.EE.C.8B