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Terms in this set (20)
System of Linear Equations in 2 Variables:
Each linear equation in two variables defined a straight line.
Solution of a System of Linear Equations:
To solve a system of two linear equations in two variables, we graph both equations in the same coordinate system. The coordinates of any points that graphs have in common are solutions to the system, since they satisfy both equations.
Substitution Method:
The method of solving "by substitution" works by solving one of the equations (you choose which one) for one of the variables (you choose which one), and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other.
Linear Combination Method:
a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).
System of Linear Inequalities in 2 Variables:
A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.
Solution of a System of Linear Inequalities:
"Solving" systems of linear inequalities means "graphing each individual inequality, and then finding the overlaps of the various solutions".
Graph of a System of Linear Inequalities:
graph each inequality, and then find the overlapping portions of the solution regions.
Optimization:
a mathematical technique for finding a maximum or minimum value of a function of several variables subject to a set of constraints, as linear programming or systems analysis.
Linear Programming:
a mathematical technique for maximizing or minimizing a linear function of several variables, such as output or cost.
Objective Function:
(in linear programming) the function that it is desired to maximize or minimize.
Constraints:
a constraint is a condition of an optimization problem that the solution must satisfy. There are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. The set of candidate solutions that satisfy all constraints is called the feasible set.
Feasible Region:
a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints.
3D Coordinate System:
A coordinate system in which the coordinates of a point are its distances from a set of perpendicular lines that intersect at an origin, such as two lines in a plane or three in space.
Z-Axis:
The axis in three-dimensional Cartesian coordinates which is usually oriented vertically. Cylindrical coordinates are defined such that the -axis is the axis about which the azimuthal coordinate is measured.
Ordered Triple:
Ordered triples which are defined as ordered pairs do not have this property with respect to ordered pairs.
Octants:
an arc of a circle equal to one eighth of its circumference, or the area enclosed by such an arc with two radii of the circle.
Linear Equation in 3 Variables:
a first-order equation involving two variables: its graph is a straight line in the Cartesian coordinate system. any equation such that the sum of two solutions is a solution, and a constant multiple of a solution is a solution. Compare linear operator.
Function of 2 Variables:
A real-valued function f of two variables is a rule which assigns to each ordered pair (x, y) in D a unique real number denoted f (x, y). 2. The set D is called the domain of f. Usually, when defining a function, one must also specify its domain.
System of 3 Linear Equations in 3 Variables:
Solving Systems by Addition. A "system" of equations is a set or collection of equations that you deal with all together at once. Linear equations (ones that graph as straight lines) are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables.
Solution of a System if 3 Linear Equations:
Solving Systems by Addition. A "system" of equations is a set or collection of equations that you deal with all together at once. Linear equations (ones that graph as straight lines) are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables.
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