# Study sets matching "term:algebra = solutions"

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statements are unlike equations because…

finite number of solutions, each is cal…

quadratic equation

to quickly find the roots of a quadrati…

equals sign

root

x=-b±√(b²-4ac)/2a

factorise

statements are unlike equations because…

equals sign

finite number of solutions, each is cal…

root

If D ≠ 0

If D = 0, Dy ≠ 0

If D = 0, Dy = 0

discriminant is positive

graphs intersect; consistent independent

graphs are parallel; inconsistent

graphs coincide; consistent dependent; IMF

two different rational numbers

If D ≠ 0

graphs intersect; consistent independent

If D = 0, Dy ≠ 0

graphs are parallel; inconsistent

consistent equations

dependent equations

equivalent equations

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 a…

equations having all common solutions

a system of linear equations that do not contain any common po…

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 a…

absolute value

IxI symbol means:

Select the graph for the solution of th…

Select the graph for the solution of th…

the distance from zero on the number line

the absolute value of some number x

no solution

https://internationalvla.sooschools.com/media/g_alg01_ccss_201…

absolute value

the distance from zero on the number line

IxI symbol means:

the absolute value of some number x

Equation

(A acute) a is greater than or equal to…

(A acute) (a is less than b) a is less…

(A acute) (a is less than b) a is equal…

h = b sin A

one triangle

no solution

one solution

Equation

h = b sin A

(A acute) a is greater than or equal to…

one triangle

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 a…

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 a…

consistent independent solution

consistent dependent

inconsistent system

system of linear equations

-exactly one solution... -lines intersect ... -lines are distinct

-same line... -infinitely many solutions... -same slope and y-interc…

-parallel(same slope)... -no solution... -same slope dif y-int

consists of 2 or more linear equations in the same variables

consistent independent solution

-exactly one solution... -lines intersect ... -lines are distinct

consistent dependent

-same line... -infinitely many solutions... -same slope and y-interc…

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.

Homogeneous coordinates

Homogeneous equation

Homogeneous form

Trivial Solution

In R3 the representation of (x,y,z) as (X,Y,Z,H) for and H ≠ 0…

An equation of the form Ax = 0. Possibly written as a vector e…

Of (a vector) v in R^n. The point v = [v... 1] in R^n+1

The solution x = 0 of a homogeneous equation Ax = 0.

Homogeneous coordinates

In R3 the representation of (x,y,z) as (X,Y,Z,H) for and H ≠ 0…

Homogeneous equation

An equation of the form Ax = 0. Possibly written as a vector e…

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

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

#8. The Graph to the above equation.

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

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

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

#57. Write the quadratic function repre…

#60. Write the quadratic function repre…

#62. Use zeros to graph the function.…

#68. Use zeros to graph the function.…

#57. Write the quadratic function repre…

#60. Write the quadratic function repre…

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 multipli…

when a number outside parentheses multiples with all the terms…

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

additive inverse

algebraic expression

associative property

The distance between a real number and zero on a number line.

The opposite of a number. When added together, the sum is zero.

A collection of numbers and variables with at least one arithm…

The grouping of terms within expressions involving addition or…

absolute value

The distance between a real number and zero on a number line.

additive inverse

The opposite of a number. When added together, the sum is zero.

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 multipli…

when a number outside parentheses multiples with all the terms…

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 multipli…

when a number outside parentheses multiples with all the terms…

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 proportion…

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.