Math 3 Ch. 05.1 Systems Of Linear Equations

Front 1

Give the formula for a linear equation in two variables in standard form:

Back 1

Ax + By = C
Where A, B, and C are real numbers and A and B cannot BOTH be zero.

Front 2

How many solutions are there to a linear equation in two variables?

Back 2

infinite

Front 3

Any collection of two or more equations is called:

Back 3

A system of equations.

Front 4

The Solution Set of a system of linear equations in two variables is:

Back 4

the set of all ordered pairs that satisfy BOTH equations of the system.

Front 5

What are the types of systems of equations?

Back 5

Consistent and Inconsistent.
There are two types of consistent equations and one type of inconsistent equations.

Front 6

What are the two types of consistent equations?

Back 6

Independent and Dependent

Front 7

Describe each type of system:

Back 7

Consistent equations: Have at least one solution; there are two types: Independent and Dependent.
Independent equations have EXACTLY one solution. Dependent equations have INFINITELY MANY solutions.
Inconsistent equations: have no solutions.

Front 8

How is the solution set to an Independent system of equations written?
ie... If (-2,4) is the ordered pair of the solution?

Back 8

The solution set is written as an ordered pair inside set notation; {(-2,4)}

Front 9

How is the solution set to a Dependent system of equations written?
ie... if the system is the two equations is:
3x - y = 2 and 2y - 6x = -4

Back 9

The solution set is written in set-builder notation with the ordered pair as the
"element " and the first equation {(x,y)|3x - y = 2} following "such that."

Front 10

What are the steps in solving systems of linear equations by the substitution method?

Back 10

1) Take the first equation and isolate one variable.
2) Plug in this isolated equation into the second equation.
3) Once you find one variable, plug it into the isolated equation to find the second variable.

Front 11

Two systems with the same solution set are called:

Back 11

equivalent systems.

Front 12

Describe the results for each type of system when solved using the substitution or elimination methods:

Back 12

Independent systems = an ordered pair
Dependent systems = an identity
Inconsistent systems = a false statement

Front 13

What is the formula for finding the slope of a linear equation given in standard form?

Back 13

If Ax + By = C,
m = -A/B

Front 14

What is the formula for finding the y-intercept of a linear equation given in standard form?

Back 14

If Ax + By = C,
y-intercept = C/B