# algebra ii honors chapter 3 Flashcards

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Systems of Equations

Linear System

Solution of a System

Inconsistent System

A set of two or more equations with the same variables

A system of equations containing only linear equations

A set of values for the variables that makes all the equations…

No solution

Systems of Equations

A set of two or more equations with the same variables

Linear System

A system of equations containing only linear equations

Coefficient

Constant Term

Polynomial

Binomial

When variable(s) are multiplied by a number, the number is cal…

A number that is not multiplied by a variable. In the expressi…

An algebraic expression that involves at most the operations o…

An expression that is the sum or difference of exactly two ter…

Coefficient

When variable(s) are multiplied by a number, the number is cal…

Constant Term

A number that is not multiplied by a variable. In the expressi…

parallel lines

transversal line

corresponding angles

supplementary angles

lines in the same plane that never intersect

Line that crosses two or more parallel lines.

Angles in the same place on different lines

Two angles whose sum is 180 degrees

parallel lines

lines in the same plane that never intersect

transversal line

Line that crosses two or more parallel lines.

System of equations

Point of intersection

Consistent system

Inconsistent system

equations with the same solution

point on graph that is solution for both equations

at least one solution system

no solutions system

System of equations

equations with the same solution

Point of intersection

point on graph that is solution for both equations

independent system

dependent system

inconsistent system

≤ or ≥ will be

ONLY one solution

infinitely many solutions... THEY ARE THE SAME EXACT LINE

no solution... parallel lines... slope is the same

solid

independent system

ONLY one solution

dependent system

infinitely many solutions... THEY ARE THE SAME EXACT LINE

system of equations

If (2,1) is a solution of both equation…

What are the 3 possible outcomes of gra…

How do you list the solution of coincid…

A set of equations.

an apparent solution

intersecting lines, parallel lines, or coincident lines

{ (x,y) | ax+by=c }

system of equations

A set of equations.

If (2,1) is a solution of both equation…

an apparent solution

bounded region

consistent system

constraints

dependent system

when the graph of a system of constraints is a polygonal region

a system of equations or inequalities that has at least one so…

restrictions placed on potential solutions to a problem

a system of equations that has infinitely many solutions

bounded region

when the graph of a system of constraints is a polygonal region

consistent system

a system of equations or inequalities that has at least one so…

Bounded

Break-even point

Consistent

Dependent

When the feasible region is enclosed

Is the point at which the income equals the cost

It has at least one solution

If it has an infinite number of solutions

Bounded

When the feasible region is enclosed

Break-even point

Is the point at which the income equals the cost

if you are solving a system of equation…

if you are solving a system of equation…

if you are solving a system of equation…

If your first step in solving a system…

elimination

consistent

dependent

substitution

if you are solving a system of equation…

elimination

if you are solving a system of equation…

consistent

system of two linear equations

consistent

inconsistent

independent

In two variables x and y, also called a linear system, consist…

A system that has at least one solution

A system that has no solution

A consistent system that has exactly one solution

system of two linear equations

In two variables x and y, also called a linear system, consist…

consistent

A system that has at least one solution

Function of two variables

Linear Combination

Linear Equation in three variables

Linear Programming

A relationship in which one variable depends on two other vari…

If neither variable has a coefficient of 1 or -1

x,y, and z in an equation form where a, b, c are not all zero

The process of optimizing a linear objective function subject…

Function of two variables

A relationship in which one variable depends on two other vari…

Linear Combination

If neither variable has a coefficient of 1 or -1

Bounded

coefficient matrix

column matrix

consistent

A region is bounded when the graph of a system of constraints…

a matrix that contains only the coefficients of a system of eq…

a matrix that has only one column

a system of equations that has at least one ordered pair that…

Bounded

A region is bounded when the graph of a system of constraints…

coefficient matrix

a matrix that contains only the coefficients of a system of eq…

break-even point

systems of equations

consistent

inconsistent

the point at which the income equals the cost

a set of equations with the same variables

a system of equations that has at least one ordered pair that…

a system of equations with no ordered pair that satisfies both…

break-even point

the point at which the income equals the cost

systems of equations

a set of equations with the same variables

Completing the square

Complex conjugates

Complex number

Constant term

A process used to make a quadratic expression into a pergevt s…

Two complex number of the form a+bi and a-bi

Any number that can be written innthe form a+bi, where a and b…

In f(x)= ax^2 + bx + c, c is the ___________

Completing the square

A process used to make a quadratic expression into a pergevt s…

Complex conjugates

Two complex number of the form a+bi and a-bi

Addition Property of Equality

Subtraction Property of Equality

Transformation by Substitution

Transformation by Addition

Substitute an equivalent expression for any expression in a gi…

Add the same real number to each side of a given equation.

Addition Property of Equality

Subtraction Property of Equality

system of two linear equations

consistent

Inconsistent

Independent

two equations that can be written in the following forms... ax+by…

a system that has at least one solution

A system with no solution

A consistent system that has exactly one solution

system of two linear equations

two equations that can be written in the following forms... ax+by…

consistent

a system that has at least one solution

bounded region

consistent system

constraints

dependent system

when the graph of a system of constraints is a polygonal region

a system of equations that has at least one solution

the inequalities we graph

a consistent system that has an infinite number of solutions (…

bounded region

when the graph of a system of constraints is a polygonal region

consistent system

a system of equations that has at least one solution

System of equations

Linear system

Solution of a system

System of inequalities

A set of two or more equations

Consists of linear equations

A set of values for the variables that makes all the equations…

Set of inequalities (linear or otherwise) solutions is any ord…

System of equations

A set of two or more equations

Linear system

Consists of linear equations

Continuous Graph

Discrete Graph

Relation

Domain

Graphs that are connected lines or curves

Graphs that are distinct points

Relationships between two or more variables.

The set of all x-values in a relation

Continuous Graph

Graphs that are connected lines or curves

Discrete Graph

Graphs that are distinct points

Monomial

Polynomial

Degree of a monomial

Degree of a polynomial

a number or a product of numbers and variables

a monomial or sum or difference of monomials

the sum of the exponents of the variables

the degree of the term with the highest degree

Monomial

a number or a product of numbers and variables

Polynomial

a monomial or sum or difference of monomials

inequality

roster form

set-builder notation

universal set

A mathematical sentence that contains a combination of numbers…

Lists the elements of a set within braces {}

Describes the properties an element must have to be included i…

The largest set

inequality

A mathematical sentence that contains a combination of numbers…

roster form

Lists the elements of a set within braces {}