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.

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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.

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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.

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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.

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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.

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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.

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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.