# Study sets matching "term:algebra = solutions"

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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 system

inconsistent system

independent system

dependent system

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

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

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

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

consistent system

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

inconsistent system

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

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…

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 soluti…

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.

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.

#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…

solution

a=b

x=a

a=a

a value that when in place of a variable holds the equation to…

no values of the variable for which the equation is true

the equation is true for exactly one value of the variables

the equation is true for all values of the variable

solution

a value that when in place of a variable holds the equation to…

a=b

no values of the variable for which the equation is true

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)

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.

System of Equations

Solution

Linear Combination

Elimination

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

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

Another for Elimination Method of solving systems

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

System of Equations

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

Solution

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