# Study sets matching "1 algebra linear equations"

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coordinate plane

origin

x-axis

y-axis

the grid created by the horizontal x-axis and the vertical y-a…

(0,0) in the coordinate plane; center of the grid

the horizontal number line in the coordinate plane (left to ri…

the vertical number line in the coordinate plane (up and down)

coordinate plane

the grid created by the horizontal x-axis and the vertical y-a…

origin

(0,0) in the coordinate plane; center of the grid

elimination method

linear inequality

solution of a system of linear inequali…

solution of a system of linear equations

solving systems by adding or subtracting equations to eliminat…

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 eliminat…

linear inequality

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

rise

run

slope

dependent

vertical change... the difference in the y-values on a line

horizontal change... the difference in the x-values on a line

Slope= Rise/Run=Change in Y/Change in X... m = y₂-y₁/ x₂-x₁

Variable that changes as a result of a change in the independe…

rise

vertical change... the difference in the y-values on a line

run

horizontal change... the difference in the x-values on a line

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

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 variabl…

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?... y=4x-3... y=-5x+6

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

consistent system

dependent system

elimination method

inconsistent system

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

a system of equations that has infinitely many solutions

a method used to solve systems of equations in which one varia…

a system of equations or inequalities that has no solution

consistent system

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

dependent system

a system of equations that has infinitely many solutions

consistent system

dependent system

elimination method

inconsistent system

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

a system of equations that has infinitely many solutions

a method used to solve systems of equations in which one varia…

a system of equations or inequalities that has no solution

consistent system

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

dependent system

a system of equations that has infinitely many solutions

Linear Equation

Standard Form

Rules of Standard Form

To graph on a calculator

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

Ax + By = C

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

Y=, enter the number, GRAPH

Linear Equation

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

Standard Form

Ax + By = C

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

affine transformation

augmented matrix

back substitution

basic variable

similar to a linear transformation, but does not necessarily p…

a matrix made up of a coefficient matrix for a linear system a…

phase of row reduction which transforms an echelon matrix to a…

a variable in the linear system that corresponds to a pivot co…

affine transformation

similar to a linear transformation, but does not necessarily p…

augmented matrix

a matrix made up of a coefficient matrix for a linear system a…

solution of a system of linear inequali…

system of linear inequalities

Consistent

independent

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

a set of two or more linear inequalities with the same variabl…

system of equations with at least one solution

system that has exactly one solution

solution of a system of linear inequali…

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

system of linear inequalities

a set of two or more linear inequalities with the same variabl…

System of linear equations

Solve graphically

Solution to a system of linear equations

Infinite solutions

2 or more linear equations

Use a graph to find the solution

The point at which 2 linear equations intersect.

The number of solutions a system has when the graphs of the eq…

System of linear equations

2 or more linear equations

Solve graphically

Use a graph to find the solution

What is a linear equation?

What is a system of linear equations?

What is a solution of a linear equation?

What is a solution set?

Any equation that can be written in the following form: (pg. 2)

A system of linear equations (or a linear system) is a collect…

A list of numbers that satisfies a system of linear equations.…

The set of all possible solutions is called the solution set o…

What is a linear equation?

Any equation that can be written in the following form: (pg. 2)

What is a system of linear equations?

A system of linear equations (or a linear system) is a collect…

The slope of the line passing through p…

The slope of the line passing through p…

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 p…

m = 0

The slope of the line passing through p…

Slope is Undefined

Equation

Equivalent Equations

Identity

Inverse operations

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

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 ex…

Equivalent Equations

Equations that have the same solution as the original equation

Linear Equation

Linear System

Solution

Solution Set

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

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

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

The set of all possible solutions for a given system

Linear Equation

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

Linear System

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