# algebra ii honors chapter 3 Flashcards

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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 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

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

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

linear programming... constraints

boundary lines

consistent independent

inconsistent

a method of finding a minimum or maximum value that satisfies…

When graphing an inequality in two variables, the ______ _____…

If the equations in a system have different slopes the system…

If the equations in a system have equal slopes and equal y-int…

linear programming... constraints

a method of finding a minimum or maximum value that satisfies…

boundary lines

When graphing an inequality in two variables, the ______ _____…

Consistent Independent

Consistent Dependent

Inconsistent

Graphing to solve a system

"1 solution"... Slopes are different

"infinitely many solutions"... Same slope and y intercept

"No solution"... Same slope different y intercept

Graph the equations and the answer is where the two lines inte…

Consistent Independent

"1 solution"... Slopes are different

Consistent Dependent

"infinitely many solutions"... Same slope and y intercept

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

Absolute value

Axes

Base of a power

binomial

the distance from 0 on the number line

x & y axis intersecting at the origin (0,0)

the repeated factor of the power

a polynomial with 2 terms

Absolute value

the distance from 0 on the number line

Axes

x & y axis intersecting at the origin (0,0)

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

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 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

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

root of an equation

zero of a function

Complex Number

Imaginary Number

A solution of an equation. ... Ex. The roots of x²-x-6 = 0 are x…

An x-value of a function f for which f(x) = 0. ... Ex: The zeroes…

A number written in the form a + bi, where a and b are real nu…

A number written in the form a + bi, where a and b are real nu…

root of an equation

A solution of an equation. ... Ex. The roots of x²-x-6 = 0 are x…

zero of a function

An x-value of a function f for which f(x) = 0. ... Ex: The zeroes…

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

polynomials

square a number

first difference

second difference

an expression of more than 2 algebraic terms.

...to multiply a number by itself or to raise it to the power…

Values obtained by subtracting each term in a sequence from it…

Differences that are found by subtracting consecutive first di…

polynomials

an expression of more than 2 algebraic terms.

square a number

...to multiply a number by itself or to raise it to the power…

Bounded

Break even point

Coefficient matrix

Consistent

Feasible region is enclosed

Is the point which income equals cost

Is a matrix that contains only the coefficients of the system

If it has at least 1 solution

Bounded

Feasible region is enclosed

Break even point

Is the point which income equals cost

system of equations

linear system

solution of a system

one solution

a set of two or more equations using the same variables

a set of two or more linear equations that use the same variab…

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

intersect at one point

system of equations

a set of two or more equations using the same variables

linear system

a set of two or more linear equations that use the same variab…