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elimination method

linear inequality

solution of a system of linear inequal…

solution of a system of linear equations

solving systems by adding or subtracting equations to elimina…

an inequality in two variables whose graph is a region of the…

a set of values that make all inequalities in a system true.…

a set of values that make all equations in a system true. [p.…

elimination method

solving systems by adding or subtracting equations to elimina…

linear inequality

an inequality in two variables whose graph is a region of the…

coefficient

distributive property

equation

inequality

the numerical part of a term

for any numbers a, b, and c: a(b+c) = ab+bc

a mathematical sentence showing two expressions are equal

mathematical sentences having the symbols <,>

coefficient

the numerical part of a term

distributive property

for any numbers a, b, and c: a(b+c) = ab+bc

Systems of Linear Equations

Solution of a System of Linear Equations

Consistent System of Linear Equations

Inconsistent System of Linear Equations

two or more linear equations involving the same variables.

An ordered pair that satisfies each equation in a system of l…

A system of equations that has at least one solution.

A system of equations that has no solutions. The equations ha…

Systems of Linear Equations

two or more linear equations involving the same variables.

Solution of a System of Linear Equations

An ordered pair that satisfies each equation in a system of l…

conjecture

theorem

rule

linear equation in one variable

An unproven statement about a general mathematical concept, e…

A proven statement about a general mathematical concept.

A term used in place of the word theorem.

An equation that can be written as ax + b = 0, where a ≠ 0.

conjecture

An unproven statement about a general mathematical concept, e…

theorem

A proven statement about a general mathematical concept.

linear equation in one variable

solution of an equation

inverse operation for addition

inverse operation for subtraction

An equation that can be written as ax + b = 0, where a ≠ 0.

a value that makes the equation true

subraction

addition

linear equation in one variable

An equation that can be written as ax + b = 0, where a ≠ 0.

solution of an equation

a value that makes the equation true

Function

Function Notation

Input

Output

A relationship where each input has exactly one output.

If x is input and y is the output, then the function notation…

A number in the domain of a function. ... The independent variab…

A number in the range of a function.... The dependent variable.

Function

A relationship where each input has exactly one output.

Function Notation

If x is input and y is the output, then the function notation…

x<-9

8

(1, 1)

x<2 or x >20

Solve this inequality:... (hint: flip the symbol when you ÷ or ×…

Solve for x:... 4(x-5)=12

What is the solution?... (hint: 2nd, CALC, 5, enter, enter, ente…

Solve this compound "or" inequality:... 5x<10 or .5x>10

x<-9

Solve this inequality:... (hint: flip the symbol when you ÷ or ×…

8

Solve for x:... 4(x-5)=12

The slope of the line passing through…

The slope of the line passing through…

Slope

Y-Intercept

m = 0

Slope is Undefined

The steepness of a line

Where a line crosses the y-axis

The slope of the line passing through…

m = 0

The slope of the line passing through…

Slope is Undefined

The slope of the line passing through…

The slope of the line passing through…

The slope of the line passing through…

Slope

m = 0

Slope is Undefined

m = 1

The steepness of a line

The slope of the line passing through…

m = 0

The slope of the line passing through…

Slope is Undefined

Linear Equation

Linear System

Solution

Solution Set

An equation that can be written in the form:... a1x1+a2x2+...+an…

A collection of one or more linear equations involving the sa…

A list (s1, s2, ..., sn) of numbers that makes each equation…

The set of all possible solutions for a given system

Linear Equation

An equation that can be written in the form:... a1x1+a2x2+...+an…

Linear System

A collection of one or more linear equations involving the sa…

x<-9

8

(1, 1)

x<2 or x >20

Solve this inequality:... (hint: flip the symbol when you ÷ or ×…

Solve for x:... 4(x-5)=12

What is the solution?... (hint: 2nd, CALC, 5, enter, enter, ente…

Solve this compound "or" inequality:... 5x<10 or .5x>10

x<-9

Solve this inequality:... (hint: flip the symbol when you ÷ or ×…

8

Solve for x:... 4(x-5)=12

When is a system of linear equations c…

When is a system of linear equations i…

When do 2 linear systems have the same…

(Row) Echelon Form

When it has either one solution or infinitely many solutions

When it has no solution

If their augmented matrices are row equivalent

1) All nonzero rows are above any rows of all zeros... 2) Each l…

When is a system of linear equations c…

When it has either one solution or infinitely many solutions

When is a system of linear equations i…

When it has no solution

Equation

Equivalent Equations

Identity

Inverse operations

a statement formed when an equal sign is placed between two e…

Equations that have the same solution as the original equation

An eqaution that is true for all values of the variables

operations that undo each other

Equation

a statement formed when an equal sign is placed between two e…

Equivalent Equations

Equations that have the same solution as the original equation

Linear Equation

Standard Form

Rules of Standard Form

To graph on a calculator

An equation that forms a straight line when graphed. It does…

Ax + By = C

- A has to be greater than or equal to zero... - A and B are bot…

Y=, enter the number, GRAPH

Linear Equation

An equation that forms a straight line when graphed. It does…

Standard Form

Ax + By = C

conjecture

theorem or rule

equation

linear equation in one variable

an unproven statement about a general mathematical concept

a proven statement about a general mathematical concept

a statement that two expressions are equal

an equation that can be written in the form ax + b = 0, where…

conjecture

an unproven statement about a general mathematical concept

theorem or rule

a proven statement about a general mathematical concept

parallel lines

perpendicular lines

linear inequality in two variables

solution of an inequality in two varia…

Two different non-vertical lines that have the same slope

Two non-vertical lines in the same plane whose slopes have a…

Can be written in one of the following forms: Ax + By < C, Ax…

One or more ordered pairs that make the inequality true.

parallel lines

Two different non-vertical lines that have the same slope

perpendicular lines

Two non-vertical lines in the same plane whose slopes have a…

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…

x<-9

8

(1, 1)

x<2 or x >20

Solve this inequality:... (hint: flip the symbol when you ÷ or ×…

Solve for x:... 4(x-5)=12

What is the solution?... (hint: 2nd, CALC, 5, enter, enter, ente…

Solve this compound "or" inequality:... 5x<10 or .5x>10

x<-9

Solve this inequality:... (hint: flip the symbol when you ÷ or ×…

8

Solve for x:... 4(x-5)=12

Slope-Intercept Form of an Equation

Point-Slope Form

Family of Functions

Parent Function

If a line has slope m and y-intercept (0, b), then the line i…

The line with slope m that contains the point (x₁, y₁) can be…

A set of functions whose graphs have basic characteristics in…

The most basic function of a family of functions.

Slope-Intercept Form of an Equation

If a line has slope m and y-intercept (0, b), then the line i…

Point-Slope Form

The line with slope m that contains the point (x₁, y₁) can be…

Graphically, a system of equations has…

Graphically, a system of equations has…

The three possible solutions for a sys…

A system has infinite solutions if:

They are parallel lines. They never intersect so there's no w…

at the point of intersection. The point where lines have a co…

- no solution... - infinite solutions ... - a unique solution

The equations are equal.... Same slope and y-intercept.

Graphically, a system of equations has…

They are parallel lines. They never intersect so there's no w…

Graphically, a system of equations has…

at the point of intersection. The point where lines have a co…

Subtraction Property of Equality

Addition Property of Equality

Division Property of Equality

Multiplication Property of Equality

If a = b, then a - c = b - c. Subtracting equal amounts from…

If a = b, then a + c = b + c. Adding equal amounts to each si…

If a = b and c does not equal 0, then a/c = b/c. Dividing eac…

If A = B, then A**C = B**C. Multiplying each side of an equatio…

Subtraction Property of Equality

If a = b, then a - c = b - c. Subtracting equal amounts from…

Addition Property of Equality

If a = b, then a + c = b + c. Adding equal amounts to each si…

Addition property of equality

Subtraction property of equality

Multiplication property of equality

Division property of equality

Add the same quantity (amount) to both sides, and the equatio…

Subtract the same quantity (amount) from both sides, and the…

Multiply both sides of an equation by the same quantity (amou…

Divide both sides of an equation by the same quantity (amount…

Addition property of equality

Add the same quantity (amount) to both sides, and the equatio…

Subtraction property of equality

Subtract the same quantity (amount) from both sides, and the…

slope intercept form

point slope form

y - intercept

How to Write a Linear Function... Ex: Wri…

where m is the slope and (x1, y1) is a point on the line... Thi…

the y-coordinate of the point where the line crosses the y-axis

1 - Write ƒ(0) = 5 as (0, 5) and ƒ(4) = 17 as (4, 17)... 2 - Cal…

slope intercept form

point slope form

where m is the slope and (x1, y1) is a point on the line... Thi…

The Rectangular Coordinate System

On the x-axis

On the y-axis

We can represent a specific location,…

is made up of a horizontal number line and a vertical number…

the positive direction is to the right and the negative direc…

the positive direction is up and the negative direction is do…

These two numbers make up an ordered pair; we write an ordere…

The Rectangular Coordinate System

is made up of a horizontal number line and a vertical number…

On the x-axis

the positive direction is to the right and the negative direc…

linear equation

slope

y-intercept

x-intercept

An equation in two variables whose graph is a straight line.

The steepness of a line. A ratio comparing the change in y ov…

The point where a graph crosses the y-axis. The value of the…

The point where a graph crosses the x-axis. The value of the…

linear equation

An equation in two variables whose graph is a straight line.

slope

The steepness of a line. A ratio comparing the change in y ov…

System of Equations

System of Inequalities

Consistent

Inconsistent

A set of equations with the same variables.

A set of two or more inequalities with the same variables

A system of equations that has at least one solution is consi…

A system of equations that has no solution.

System of Equations

A set of equations with the same variables.

System of Inequalities

A set of two or more inequalities with the same variables

system of linear equations

solution of a system

elimination method

substitution method

Two or more linear equations using the same variables.

Any ordered pair (x,y) that makes both equations true in a sy…

A method for solving systems by adding or subtracting equatio…

A method for solving systems by replacing one variable with a…

system of linear equations

Two or more linear equations using the same variables.

solution of a system

Any ordered pair (x,y) that makes both equations true in a sy…

Additive Identity

Distributive Property

Literal Equation

Multiplicative Identity

the number 0 (for the real numbers)

a(b + c) = ab + ac or a(b - c) = ab - ac

equation containing more than one variable

the number 1 (for the real numbers)

Additive Identity

the number 0 (for the real numbers)

Distributive Property

a(b + c) = ab + ac or a(b - c) = ab - ac

The Rectangular Coordinate System

On the x-axis

On the y-axis

We can represent a specific location,…

is made up of a horizontal number line and a vertical number…

the positive direction is to the right and the negative direc…

the positive direction is up and the negative direction is do…

These two numbers make up an ordered pair; we write an ordere…

The Rectangular Coordinate System

is made up of a horizontal number line and a vertical number…

On the x-axis

the positive direction is to the right and the negative direc…

Formula

Solve an Equation

Equivalent Equations

Multi-Step Equations

A mathematical relationship or rule expressed in symbols.

The process of finding all values of the variable that make t…

equations that have the same solution

Equations with more than one operation.

Formula

A mathematical relationship or rule expressed in symbols.

Solve an Equation

The process of finding all values of the variable that make t…

slope intercept form

constant function

constraint

linear extrapolation

the equation of a straight line in the form y = mx + b where…

Consistent horizontal, slope = 0 (Horizontal line)

a condition that a solution must satisfy

The use of a linear equation to predict values that are outsi…

slope intercept form

the equation of a straight line in the form y = mx + b where…

constant function

Consistent horizontal, slope = 0 (Horizontal line)

slope intercept form

point slope form

y - intercept

How to Write a Linear Function... Ex: Wri…

where m is the slope and (x1, y1) is a point on the line... Thi…

the y-coordinate of the point where the line crosses the y-axis

1 - Write ƒ(0) = 5 as (0, 5) and ƒ(4) = 17 as (4, 17)... 2 - Cal…

slope intercept form

point slope form

where m is the slope and (x1, y1) is a point on the line... Thi…

algebraic expression

numerical expression

like terms

absolute value

an expression that contains at least one variable

An expression that contains only numbers and operations

Expressions that contain the same variables to the same power

The distance a number is from zero on a number line

algebraic expression

an expression that contains at least one variable

numerical expression

An expression that contains only numbers and operations

linear equation

expression

equation

coefficient

An equation in two variables whose graph in a coordinate plan…

A mathematical sentence without an equal sign.

A mathematical sentence that contains an equal sign.

A number multiplied by a variable in an algebraic expression…

linear equation

An equation in two variables whose graph in a coordinate plan…

expression

A mathematical sentence without an equal sign.

inconsistent equation

consistent equation

identity

equivalent equations

an equation with no solution

an equation with one solution

an equation that is true for all values of the variable

equations that have the same solution... EX: x+1=9 and x-2=6 bot…

inconsistent equation

an equation with no solution

consistent equation

an equation with one solution

How can a linear system and their prop…

R^n

Vectors in R^2 represents:

Geometric interpretation

Using th concept of vectors

the set of all vectors of size n?

v = (v1, v2)

u + v represented by a diagonal arrow in a parallelogram

How can a linear system and their prop…

Using th concept of vectors

R^n

the set of all vectors of size n?