Writing Systems 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 to solve a system of equations?

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To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

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What is the substitution method in solving systems of equations?

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The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

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What is the elimination method in solving systems of equations?

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

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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 less than, greater than, less than or equal to, or greater than or equal to the other.

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How do you represent a system of inequalities graphically?

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A system of inequalities is represented graphically by shading the regions of the graph that satisfy all inequalities in the system.

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

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A linear equation represents a straight line, while a linear inequality represents a region of the graph where the inequality holds true.

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

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A feasible solution is a solution that satisfies all constraints (inequalities) in the system.

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How can you check if a point is a solution to a system of equations?

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To check if a point is a solution, substitute the point's coordinates into each equation. If all equations are satisfied, the point is a solution.

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What is the graphical method for solving a system of equations?

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The graphical method involves plotting each equation on a graph and identifying the point(s) where the lines intersect.