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.

Front

What does it mean for two lines to be parallel in a linear system?

Back

Two lines are parallel if they have the same slope and will never intersect, resulting in no solutions.

Front

What is the solution to a system of equations?

Back

The solution to a system of equations is the point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

What is an objective function in linear programming?

Back

An objective function is a mathematical expression that defines the goal of optimization, typically to maximize or minimize a quantity.

Front

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

Back

Substitute the point's coordinates into each equation; if all equations are satisfied, the point is a solution.

Front

What is the graphical representation of a linear equation?

Back

A linear equation can be represented graphically as a straight line on a coordinate plane.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

Front

What is the significance of the vertices in a linear programming problem?

Back

The vertices of the feasible region are where the maximum or minimum values of the objective function occur.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you solve a system of equations using substitution?

Back

To solve by substitution, solve one equation for one variable and substitute that expression into the other equation.