solving 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.

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What does it mean to solve a system of equations?

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Finding the values of the variables that satisfy all equations in the system simultaneously.

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What is substitution in solving systems of equations?

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A method where one equation is solved for one variable, and that expression is substituted into the other equation.

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What is the graphical representation of a system of equations?

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The point(s) where the graphs of the equations intersect represent the solution(s) of the system.

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What is an inequality?

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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 boundary line, then shade the appropriate region based on the inequality.

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

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A linear equation has an equal sign, while a linear inequality uses inequality symbols.

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What does it mean for a solution to be a feasible region in linear programming?

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The set of all possible solutions that satisfy the constraints of the system of inequalities.

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How do you determine if a point is a solution to a system of equations?

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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 elimination method in solving systems of equations?

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