#### Study sets matching "term:algebra = solutions"

#### Study sets matching "term:algebra = solutions"

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…

equations having all common solutions

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

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…

absolute value

IxI symbol means:

Select the graph for the solution of t…

Select the graph for the solution of t…

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_20…

absolute value

the distance from zero on the number line

IxI symbol means:

the absolute value of some number x

consistent system

inconsistent system

independent system

dependent system

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

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

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

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

consistent system

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

inconsistent system

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

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…

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…

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 solut…

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.

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…

equations having all common solutions

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

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…

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

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

#8. The Graph to the above equation.

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

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

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

#57. Write the quadratic function repr…

#60. Write the quadratic function repr…

#62. Use zeros to graph the function.…

#68. Use zeros to graph the function.…

#57. Write the quadratic function repr…

#60. Write the quadratic function repr…

solution

a=b

x=a

a=a

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

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 t…

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 multipl…

when a number outside parentheses multiples with all the term…

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 proportio…

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.

(-4,-2)

(-1/5,-2)

consistent, dependent, infinitely many…

consistent, independent, one solution

2x - 3y = -2... y - 3x = 10

-10x + y = 0... 5x + 3y = -7

Classify the system of equations. Give the number of solution…

Classify the system of equations. Give the number of solution…

(-4,-2)

2x - 3y = -2... y - 3x = 10

(-1/5,-2)

-10x + y = 0... 5x + 3y = -7