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consistent system

inconsistent system

independent system

dependent system

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

a system of equations or inequalities that has no solution (s…

a system of equations that has exactly one solution (differen…

a system of equations that has infinitely many solutions (sam…

consistent system

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

inconsistent system

a system of equations or inequalities that has no solution (s…

Consistent equations

Dependent equations

Equivalent Equation

inconsistent equations

A system of linear equations that contain at least one common…

A system of linear equations that rely on each other for the…

Equations have all common solutions

a system of linear equations that do not have any points

Consistent equations

A system of linear equations that contain at least one common…

Dependent equations

A system of linear equations that rely on each other for the…

When Ax=b has no solution,

Linear system is homogenous if

Is a homogenous solution consistent or…

Trivial solution

the solution set is empty

it is of the form Ax = 0 vector in matrix equation form.

ALWAYS consistent because you can always write down the solut…

x = 0; of Ax = 0

When Ax=b has no solution,

the solution set is empty

Linear system is homogenous if

it is of the form Ax = 0 vector in matrix equation form.

#3. y=(x-1)(x+3). ... Find the x-interce…

#8. y=(x-2)(x+2). ... Graph, find the ve…

#8. The Graph to the above equation.

#13. y= x^2 -9 (x squared minus 9)... Gr…

#3. y=(x-1)(x+3). ... Find the x-interce…

#8. y=(x-2)(x+2). ... Graph, find the ve…

Homogeneous Solution:

Trivial Solution:

Nontrivial Solution:

[THEOREM] The homogeneous equation Ax…

Ax = 0; 0 is the zero vector.

the zero solution.

a nonzero vector x that satisfies Ax = 0.

the equation has at least one free variable.

Homogeneous Solution:

Ax = 0; 0 is the zero vector.

Trivial Solution:

the zero solution.

#57. Write the quadratic function repr…

#60. Write the quadratic function repr…

#62. Use zeros to graph the function.…

#68. Use zeros to graph the function.…

#57. Write the quadratic function repr…

#60. Write the quadratic function repr…

variables

constant

coefficient

Distribution

x, y, or any letter that can represent a number that changes

a number that has a set value (it is not next to a variable)

a number that is directly next to a variable... A number multipl…

when a number outside parentheses multiples with all the term…

variables

x, y, or any letter that can represent a number that changes

constant

a number that has a set value (it is not next to a variable)

Constant of Variation

Non linear

Direct Variation

Midpoint

The slope of a Direct Variation, y=kx, the "K" value

Not a line, can be a curve or a set of line segments.

A line in the form of y=kx, goes through origin, is proportio…

The point separating a line segment into two equal halves.

Constant of Variation

The slope of a Direct Variation, y=kx, the "K" value

Non linear

Not a line, can be a curve or a set of line segments.

inverse operation

equivalent equations

reciprocal

like terms

two operations that undo each other; ... addition and subtractio…

equations that have the same solution

two non-zero numbers who product is 1

terms that have the same variable parts

inverse operation

two operations that undo each other; ... addition and subtractio…

equivalent equations

equations that have the same solution

addition property of equality

algebraic expressions

division property of equality

solutions of a equation inequality

the addition property of equality state that if the same valu…

a algebraic expressions is a mathmatical pharse that uses var…

the equality states that if both sides of an equation are div…

value or values that make an equation or inequality true

addition property of equality

the addition property of equality state that if the same valu…

algebraic expressions

a algebraic expressions is a mathmatical pharse that uses var…

variable

Algebraic expression

Numerical expression

power

A symbol, usually a letter, that represents one or more value…

A mathematical phrase that includes one or more variables.

A mathematical phrase involving numbers and operations.

A number that can be expressed using a base and an exponent.

variable

A symbol, usually a letter, that represents one or more value…

Algebraic expression

A mathematical phrase that includes one or more variables.

algebraic term

constants

variables

coefficients

either a single number or a variable, or numbers and variable…

the terms in the algebraic expression that contain only numbers

unknown values, often represented by letters

the number part of the terms with variables

algebraic term

either a single number or a variable, or numbers and variable…

constants

the terms in the algebraic expression that contain only numbers

axis of symmetry

maximum point

minimum point

parabola

a line that divides a plane figure or a graph into two congru…

the vertex of a parabola that opens downwards.

the vertex of a parabola that opens upwards.

the graph of a quadratic function that forms a U-shaped curve.

axis of symmetry

a line that divides a plane figure or a graph into two congru…

maximum point

the vertex of a parabola that opens downwards.

Binomial

Coefficient

complex conjugates

complex numbers

A polynomial equation with 2 terms

A number multiplied by a variable in an algebraic expression.

Opposites of your complex number Ex: (a+bi) and (a-bi)

They are often represented as A + Bi.

Binomial

A polynomial equation with 2 terms

Coefficient

A number multiplied by a variable in an algebraic expression.

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

variables

constant

coefficient

Distribution

x, y, or any letter that can represent a number that changes

a number that has a set value (it is not next to a variable)

a number that is directly next to a variable... A number multipl…

when a number outside parentheses multiples with all the term…

variables

x, y, or any letter that can represent a number that changes

constant

a number that has a set value (it is not next to a variable)

Absolute Value

Addition

Algebraic Expression

All Real Numbers

The distance a number is from zero on the number line. |-5| = 5

The inverse operation of subtraction

An expression that contains at least one variable... 3x-4 is an…

An equation with a solution x = x

Absolute Value

The distance a number is from zero on the number line. |-5| = 5

Addition

The inverse operation of subtraction

variables

constant

coefficient

Distribution

x, y, or any letter that can represent a number that changes

a number that has a set value (it is not next to a variable)

a number that is directly next to a variable... A number multipl…

when a number outside parentheses multiples with all the term…

variables

x, y, or any letter that can represent a number that changes

constant

a number that has a set value (it is not next to a variable)

variables

constant

coefficient

Distribution

x, y, or any letter that can represent a number that changes

a number that has a set value (it is not next to a variable)

a number that is directly next to a variable... A number multipl…

when a number outside parentheses multiples with all the term…

variables

x, y, or any letter that can represent a number that changes

constant

a number that has a set value (it is not next to a variable)

reciprocal

power

exponent

base

multiplicative inverse

expression used to abbreviate repeated multiplication of the…

the number of times the base is multiplied by itself

factor to be multiplied by itself in a power

reciprocal

multiplicative inverse

power

expression used to abbreviate repeated multiplication of the…

Absolute Value

Algebraic Expression

All Real Numbers

Equation

The distance a number is from zero on the number line. |-5| = 5

An expression that contains at least one variable... 3x-4 is an…

An equation with a solution x = x

Two expressions set equal to each other

Absolute Value

The distance a number is from zero on the number line. |-5| = 5

Algebraic Expression

An expression that contains at least one variable... 3x-4 is an…

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…

consistent

dependent

elimination

inconsistent

a system of linear equations that has at least one ordered pa…

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

the use of addition or subtraction to eliminate one variable…

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

consistent

a system of linear equations that has at least one ordered pa…

dependent

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

axis of symmetry

parabola

square root property

completing the square

a line about which a figure is symmetric

the set of all points in plane that are the same distance fro…

for any real number n, if x squared = n, the x = plus or minu…

a process used to make a quadratic expression into a perfect…

axis of symmetry

a line about which a figure is symmetric

parabola

the set of all points in plane that are the same distance fro…

complement of a set

compound inequality

disjoint sets

empty set

the set of all elements in the universal set that are not in…

two or more inequalities joined together by either "and" or "…

two or more sets that do not have any elements in common. [p.…

a set with no elements. [p. 211]

complement of a set

the set of all elements in the universal set that are not in…

compound inequality

two or more inequalities joined together by either "and" or "…

factoring

term

quadratic

binomial

the process of changing a sum to a product

numbers, letters, or combinations of letters and numbers that…

an expression that can be written in the form ax(x) + bx + c,…

an expression with 2 terms

factoring

the process of changing a sum to a product

term

numbers, letters, or combinations of letters and numbers that…

equation

isolate

inverse

balance

mathematical sentence with an equal sign

to make the variable alone on one side of equation

the opposite operation

to do the same to both sides of the equation

equation

mathematical sentence with an equal sign

isolate

to make the variable alone on one side of equation

algebraic expression

base

coefficient

coordinate system

An expression consisting of one or more numbers and variables…

In an expression of the form x^n, it is the x.

The numerical factor of a term.

The grid formed by the intersection of two number lines, the…

algebraic expression

An expression consisting of one or more numbers and variables…

base

In an expression of the form x^n, it is the x.

System of Equations

Solution

Linear Combination

Elimination

A system of equations is a collection of two or more equation…

that point of intersection is called the solution to the syst…

Another for Elimination Method of solving systems

In this method you either add or subtract the equations to ge…

System of Equations

A system of equations is a collection of two or more equation…

Solution

that point of intersection is called the solution to the syst…