HA2 Linear Systems

Front

What is a linear system?

Back

A linear system is a collection of one or more linear equations involving the same variables.

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What does it mean for a point to be a solution to a linear system?

Back

A point is a solution to a linear system if it satisfies all the equations in the system.

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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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What are the possible outcomes when solving a linear system?

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The possible outcomes are: one solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (coincident lines).

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

Back

Substitute the x and y values of the point into each equation. If all equations are satisfied, the point is a solution.

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What is the substitution method in solving linear systems?

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

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What is the elimination method in solving linear systems?

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

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What is a feasible region in the context of linear inequalities?

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The feasible region is the area on a graph that satisfies all the constraints of a system of inequalities.

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What is an objective function in linear programming?

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An objective function is a mathematical expression that defines the goal of optimization, such as maximizing profit or minimizing cost.

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What does it mean to maximize a function?

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To maximize a function means to find the highest value of the function within a given set of constraints.