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equivalent systems

feasible region

linear system

matrix

two or more function systems with exactly the same solutions.

the set of ordered pairs that satisfy a system of inequalities.

a group of two or more linear equations that have the same va…

a rectangular arrangement of numbers within brackets.

equivalent systems

two or more function systems with exactly the same solutions.

feasible region

the set of ordered pairs that satisfy a system of inequalities.

system of equations

consistent

inconsistent

independent

two or more equations with the same variables

a system of equations that has at least one solution

a system of equation that has no solutions

a consistent system that has exactly one solution

system of equations

two or more equations with the same variables

consistent

a system of equations that has at least one solution

system of 2 linear equatons

solution of a system

substitution method

elimination method

A system consisting of two equations that can be written in t…

An ordered pair (x,y) that satisfies each equation of the sys…

A method of solving a system of equations by solving one of t…

A method of solving a system of equations by multiplying equa…

system of 2 linear equatons

A system consisting of two equations that can be written in t…

solution of a system

An ordered pair (x,y) that satisfies each equation of the sys…

system of two linear eqautions

solution of a system

substitution method

elimination method

a system consisting of two equations that can be written in t…

an ordered pair (x,y) that satisfies each equation of the sys…

a method of solving a system of equations by solving one of t…

a method of solving a system of equations by multiplying equa…

system of two linear eqautions

a system consisting of two equations that can be written in t…

solution of a system

an ordered pair (x,y) that satisfies each equation of the sys…

system of two linear equations

Solution of a System

Substitution method

Elimination Method

a system of two equations that can be written in the form Ax+…

an ordered pair (x, y) that satisfies each equation of the sy…

a method of solving a system of equations by solving one of t…

a method of solving a system of equations by multiplying equa…

system of two linear equations

a system of two equations that can be written in the form Ax+…

Solution of a System

an ordered pair (x, y) that satisfies each equation of the sy…

absolute value

counterexample

independent system

vertices

a number's distance from zero on the number line

a specific case that shows that a statement is false

a system of equations that has exactly one solution

the maximum or minimum values that a linear function has for…

absolute value

a number's distance from zero on the number line

counterexample

a specific case that shows that a statement is false

Solution

Inconsistant

Consistant

Consistent and Independent

The ordered pair that satisfies each equation in the system

A system with no solution, if the lines are parallel

A system with at least one solution

A system with exactly one solution

Solution

The ordered pair that satisfies each equation in the system

Inconsistant

A system with no solution, if the lines are parallel

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-in…

linear programming... constraints

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

boundary lines

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

System of two linear equations

Consistent system

Inconsistent system

Independent system

A system consisting of two equations that can be written in t…

A system of equations that has at least one solution.

A system of equations that has no solution.

A consistent system that has exactly one solution.

System of two linear equations

A system consisting of two equations that can be written in t…

Consistent system

A system of equations that has at least one solution.

Equation for arithmetic sequence

what makes an equation linear?

What is standard form?

When solving for the x intercept what…

an = a + (n - 1) d... a = first term in sequence... d = common diff…

No exponents higher than 1 ... No multiplication or division of…

Ax + By = C

y = 0

Equation for arithmetic sequence

an = a + (n - 1) d... a = first term in sequence... d = common diff…

what makes an equation linear?

No exponents higher than 1 ... No multiplication or division of…

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 zeroe…

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

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

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 zeroe…

Elimination method

System of equations

Dependent

Bounded

Eliminate one of the variable in a system of equations by add…

A set of equation with the same variables

When a system of linear equations has an infinite number of s…

A region is _____ when the graph of a system of constraints i…

Elimination method

Eliminate one of the variable in a system of equations by add…

System of equations

A set of equation with the same variables

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 i…

Differences that are found by subtracting consecutive first d…

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…

System of equations

Linear system

Solution of a system

Consistent

Two or more related unknowns as a set of two or more equations

Consists of linear equations

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

Dependent or independent answers

System of equations

Two or more related unknowns as a set of two or more equations

Linear system

Consists of linear equations

Arithmetic Sequence

Common Difference

Constant

Constant of Variation

A numerical pattern that increases or decreases at a constant…

The difference between the terms in an arithmetic sequence.

A monomial that is a real number.

The number K in equations of the form y=Kx

Arithmetic Sequence

A numerical pattern that increases or decreases at a constant…

Common Difference

The difference between the terms in an arithmetic sequence.

dependent system

equivalent system

independent system

linear system

a system of equations that has infinitely many solutions. (p.…

when you multiply each side of an equation in a system by the…

a system of equations that has exactly one solution. (p. 137)

system of equations containing only linear equations. (p. 134)

dependent system

a system of equations that has infinitely many solutions. (p.…

equivalent system

when you multiply each side of an equation in a system by the…

Relation

Function

Input

Output

A set of ordered pairs. Inputs can have different outputs (1…

A relation where every input has ONLY 1 unique output, but di…

X, domain, independent variables

Y, range, dependent variables

Relation

A set of ordered pairs. Inputs can have different outputs (1…

Function

A relation where every input has ONLY 1 unique output, but di…

Complex number

Imaginary unit i

i²

Complex numbers

Includes the set of real numbers as a subset and has i as a b…

√-1

-1

Numbers in the form a + bi, where a and b are real numbers

Complex number

Includes the set of real numbers as a subset and has i as a b…

Imaginary unit i

√-1

terminating decimal

repeating decimal

bar notation

rational number

when the division ends with a remainder of zero

when the division repeats a pattern without end

a bar that is placed over the digit(s) that repeat

any number that can be written as a fraction (ratio)

terminating decimal

when the division ends with a remainder of zero

repeating decimal

when the division repeats a pattern without end

System of Equations

Linear System

Solution of a System

Consistent System

a set of 2 or more equations

a system with linear equations

the set of values of the variable that makes all of the equat…

a system with at least one solution

System of Equations

a set of 2 or more equations

Linear System

a system with linear equations

Term

Literal Factors

Numerical Coefficient

Monomial

the product of letters, numbers, or both

the variable(s) in the term... In the monomial 7xy, the answer w…

the number that is a factor... In the monomial 7xy, the answer w…

A term with only whole numbers as exponents... Ex: 7xy, x(cubed)…

Term

the product of letters, numbers, or both

Literal Factors

the variable(s) in the term... In the monomial 7xy, the answer w…

inverse operation

equivalent equations

like terms

input

2 operations that undo each other: addition and subtraction,…

equations that have the same solution

expressions that contain the same variables to the same power

the x value, the domain

inverse operation

2 operations that undo each other: addition and subtraction,…

equivalent equations

equations that have the same solution

Constraints

Coordinate space

Dependent system

Equivalent system

Limits on the variables in the objective function in a linear…

Created by adding a third axis, the Z-access, to the XY-coord…

A system of equations that does not have a unique solution

Systems that have the same solutions

Constraints

Limits on the variables in the objective function in a linear…

Coordinate space

Created by adding a third axis, the Z-access, to the XY-coord…

linear equation

standard form

x-intercept

y-intercept

an equation that forms a line when it is graphed

Ax + By = C... "C" is called the constant. Ax + By are the varia…

the x coordinate of the point at which the graph of the equat…

the y coordinate of the point at which the graph of the equat…

linear equation

an equation that forms a line when it is graphed

standard form

Ax + By = C... "C" is called the constant. Ax + By are the varia…

system of equations

linear system

consistent system

inconsistent system

a set of two or more equations that have two or more variables

a system of equations containing only linear equations

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

a system of equations or inequalities that has no solution

system of equations

a set of two or more equations that have two or more variables

linear system

a system of equations containing only linear equations

inverse relation

simplest radical form

radical equation

index

a relation that interchanges the input and output values of t…

a radical with index n is in simplest form if the radicand ha…

an equation with one or more radicals that have variable in t…

for an integer n greater than 1, if b^n=a, then b is an nth r…

inverse relation

a relation that interchanges the input and output values of t…

simplest radical form

a radical with index n is in simplest form if the radicand ha…

System of Two Linear Equations

Solution

Consistent System

Inconsistent Solution

Consists of two equations that can be written as:... Ax + By = C…

An ordered pair (x,y) that satisfies each equation in the sys…

A system that has at least one solution.

A system that has no solutions.

System of Two Linear Equations

Consists of two equations that can be written as:... Ax + By = C…

Solution

An ordered pair (x,y) that satisfies each equation in the sys…

sequence

terms of the sequence

arithmetic sequence

common difference

a set of numbers in a specific order

the numbers of the sequence

a sequence where the difference between the successive terms…

the constant from the arithmetic sequence

sequence

a set of numbers in a specific order

terms of the sequence

the numbers of the sequence

Parent Function

Line of Best Fit

Scatterplot

Reflection

Simplest form of a set of functions that form a family

The trend line that finds the most accurate model of related…

Graph that relates two different sets of data by plotting the…

Flips the graph of a function across a line

Parent Function

Simplest form of a set of functions that form a family

Line of Best Fit

The trend line that finds the most accurate model of related…

Systems of linear equations

Solution

Consistent

Inconsistent

2 or more linear equations

for linear equations, point where graphs intersect

system that has at least one solution

system that has no solution

Systems of linear equations

2 or more linear equations

Solution

for linear equations, point where graphs intersect

inverse operation

equivalent equations

like terms

input

2 operations that undo each other: addition and subtraction,…

equations that have the same solution

expressions that contain the same variables to the same power

the x value, the domain

inverse operation

2 operations that undo each other: addition and subtraction,…

equivalent equations

equations that have the same solution

equivalent systems

feasible region

linear system

matrix

two or more function systems with exactly the same solutions.

the set of ordered pairs that satisfy a system of inequalities.

a group of two or more linear equations that have the same va…

a rectangular arrangement of numbers within brackets.

equivalent systems

two or more function systems with exactly the same solutions.

feasible region

the set of ordered pairs that satisfy a system of inequalities.

Systems of linear equations

Solution

Consistent

Inconsistent

2 or more linear equations

for systems of equations, the point where graphs intersect

system that has at least one solution

system that has no solution

Systems of linear equations

2 or more linear equations

Solution

for systems of equations, the point where graphs intersect

systems of equations

linear system

solution of a system

inconsistent system

a set of two or more equations using the same variables

a set of two or more equations using the same variables

a set of values for the variables that makes all the equation…

a type of system that has not solution(they do not touch)

systems of equations

a set of two or more equations using the same variables

linear system

a set of two or more equations using the same variables

bounded

break-even point

coefficient matrix

consistent

a region is ______ when the graph of a system of constraints…

the point at which the income equals the cost

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

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

bounded

a region is ______ when the graph of a system of constraints…

break-even point

the point at which the income equals the cost

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 i…

Differences that are found by subtracting consecutive first d…

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…

Inverse Operations

Equivalent Equations

Reciprocal

Like Terms

two operations that undo each other, such as addition and sub…

equations that have the same solution(s)

two nonzero numbers who's product is one

terms that have the same variable parts

Inverse Operations

two operations that undo each other, such as addition and sub…

Equivalent Equations

equations that have the same solution(s)

Consistent system

Constraint

Dependent system

Equivalent system

A system of linear equations that has at least one solution

restrictions on the variables of the objective function in a…

A system of equations that does not have a unique solution is…

Systems that have the same solutions

Consistent system

A system of linear equations that has at least one solution

Constraint

restrictions on the variables of the objective function in a…

Parallel lines

Skew lines

Parallel planes

Alternate interior angles

Coplanar lines that do not intersect. The symbol II means this.

Non-coplanar; they are not parallel and do not intersect.

Planes that do not intersect.

Nonadjacent interior angles that lie on opposite sides of the…

Parallel lines

Coplanar lines that do not intersect. The symbol II means this.

Skew lines

Non-coplanar; they are not parallel and do not intersect.

Consistent system

System

Subcategories of Consistent

Dependent system

system with at least one solution

2 or more equations with same set of unknowns

Dependent... independent

infinitely many solutions

Consistent system

system with at least one solution

System

2 or more equations with same set of unknowns

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 int…

Consistent Independent

"1 solution"... Slopes are different

Consistent Dependent

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

system of equations

solution of a system

consistent system

inconsistent system

a set of 2 or more equations

a set of values for the variables that makes all the equation…

has at least one solution

has no solution

system of equations

a set of 2 or more equations

solution of a system

a set of values for the variables that makes all the equation…