Zero: When there is no solution, equations are called "inconsistent"

Infinite Solution: Is when two lives overlap. "Dependent"

Bibliography:

http://www.mathwarehouse.com/algebra/linear_equation/systems-of-equation/index.php

http://www.mathsisfun.com/algebra/systems-linear-equations.html

Symbol: x=#

Identify: When the lines intercepts just once.

Ex: 2(x-1)+8=4x-20

2x-2+8=4x-20

2x+6=4x-20

2x-4x=-20-6

-2x=-26

x=13

Zero Solution: When the lines do not intercept. There's no solution.

Symbol: 0=#

Identify:

The lines are parallel

Ex: 4x+y=8
8x+2y=−14

Infinite Solution:

First Move the slider around to try to find the value of k which makes the two lines parallel.


Symbol: 0=0

Ex:

{2x-y=2

5x−+k⋅y=5


Bibliography:

http://www.ms.uky.edu/~pkoester/teaching/Fall13/MA162/Geogebra/SystemsNoAndInf.html


https://www.khanacademy.org/math/algebra2/systems_eq_ineq/systems_tutorial_precalc/e/solutions_to_systems_of_equations

One Solution: When the lines only intercept once. The lines are not parallel.

ex. 2x + 3 = 7 

Zero Solution: No solution exists, often called inconsistent. The lines are parallel.

ex. x + 4 = x + 3

Infinite Solution: Two lines over lap, it is often called inconsistent. Opposite to one solution equations. The lines intercept in every coordinate.

Ex

2x = x + x

3 = 3

(x – 2)(x + 2) = x² – 4

http://www.jamesbrennan.org/algebra/intro%20to%20algebra/solutions_of_algebraic_equations.htm

How to identify: the lines meet one time in the graph

Notation: { # }

Example: 2x+13=13

Infinite Solutions: when it looks like there is only one line, but there are 2 different lines, on top of each other, intercepting in every coordinate

How to identify: it appears to be only one line.

Notation: x|x is all real numbers

Example: 2x+3=2x+3

Zero Solutions: when the lines do not intercept, not even once

How to identify: parallel linesgoing to thebsame direction, without touching.

Notation: Ø

Example: 2x+3=2x+7

http://www.purplemath.com/modules/systlin2.htm

One solution: it occurs when two different lines (no parallel) the solution always appears in a x,y point.

EX.: x=2 {2}, y=10{10}, z=-3 {-3}

Zero solution: when there are no variables (lines are parallel)

EX.: 4=6 Ø , 10=3 Ø, 0=7 Ø

Infinite solution: when the two lines intersect in all points.

Ex.: 5=5, 9=9, 3=3 xlx is all real numbers.

http://www.mathwarehouse.com/algebra/linear_equation/systems-of-equation/index.php

-One Solution:= The line only intercepts once.

EX.

3x+7=11x+15

-Zero SolutionØ:is called inconsistent if it has no solution. And the lines are parallel they never meet.

EX.

2x+3=2x-7

-Infinite Solutions ∞You actually have 2 lines but one on top of each other so they intercept in every coordinate.

EX.

2x+3=2x+3 http://www.charleston.k12.il.us/cms/Teachers/math/PreAlgebra/paunit5/L5-4.pdf http://math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/vcalc/system/system.html

One solution: Two different non-parallel lines that cross at one point. They are called "INDEPENDENT"

Zero solution: Lines are parallel that meet. They are called "INCONSISTENT"

Infinite solution: Two lines that intercept at every coordinate. It's called "DEPENDENT"

http://www.purplemath.com/modules/systlin2.htm

http://www.mathsisfun.com/algebra/systems-linear-equations.html

How to identify: If the lines only intercepts once in the graph.

Symbol: x={#}

Example:

2. Zero Solution: This only happens when the lines are parallel. They are never going to meet.

How to identify: The lines are parallel

Symbol: 0

Example:

3. Infinite Solution: This is the rarest case and only occurs when you have the same line.

How to identify: The lines are in the same place.

Symbol: x|

Example:

Zero solution (Ø): There is no solution because the original equation is a contradiction. The equations are called "inconsistent"

Infinite solution (∞): Appears to be only one line. But it's the same line drawn twice. These "two" lines, "intersect" at every point along their length. This is called a "dependent" system, and the "solution" is the whole line.

http://www.purplemath.com/modules/systlin2.htm

http://www.mathsisfun.com/algebra/images/system-linear-types.gif

https://www.khanacademy.org/math/algebra2/systems_eq_ineq/systems_tutorial_precalc/e/solutions_to_systems_of_equations

one solution: or intersecting lines is when in a graph lines intersect once example: -7x+3=2x+2

answer:x=1/9

no solution: or inconsistent is when lines are parellel example: -7x+3=2x+2-9x

answer: 3=2

infinite solutions:or parallel lines is when linear are exactly the same example: -7x+2=2x+2-9x

answer: 0=0

https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/solutions-linear-equations/v/number-of-solutions-to-linear-equations

-One Solution: this is the most common situarion and it involves lines that intersect exactly 1 time.

Example: x-2=4

6-2=4

x=6

-Zero: This only happens when the plines are parallel. Paralleel lines are not goong to ever meet.

Example:

6x+5-2x=4+4x+1

-Infinite Solution: this is the raresy case and only occurs when you have the same line.

Consider, the 2 lines below (y=2x+1 and 2y=4x+2). These twi equations are really the same line.

Example: line 1: y= 2x+1

Line 2 2y=4x+2

One Solution: 

(x=#)

In this type of solution which is the most common one, there are two lines which intersect only one time.

We identify this solutions by having the x equal to a number.

Zero:

This types of solutions are called inconsistent, because there is no intersection between lines.

we identify it when we have a 0 equal to a number

Infinit solutions:

(∞)

This type or solutions are infinite solutions, which are two lines that overlap because they have the same slope and are located in the same y intercept.

we identify this when both numbers are the same example 0=0

Stapel, E. (2015 April 1) System of linear equations systems: Graphing.

http://www.purplemath.com/modules/systlin2.htm

The three types of solution sets:

A system of linear equations can have no solution, a unique solution or infinitely many solutions.

A system has no solution if the equations areinconsistent, they are contradictory. for example 2x+3y=10, 2x+3y=12 has no solution.

A system has aunique solution when it is consistent and the number of variables is equal to the number of nonzero rows.

A system hasinfinitely many solutions when it is consistent and the number of variables is more than the number of nonzero rows in the reference.

Zero: 2x+3y=10, 2x+3y=12

One solution: ( 2, 1, 3 ) or x=2, y=1, z=3

Infinite Solutions: has solution set (4-3z, 5+2z, z)

http://www.purplemath.com/modules/systlin2.htm

http://www.math.tamu.edu/~jlewis/Threetypesofsolsets.htm