CH 4 - SYSTEMS OF LINEAR EQUATIONS

Question 1

the graph of a line is a ________________ that satisfy the equation of the line.

Answer 1

graph of all the ordered pairs

Question 2

A system of linear equations is __________ if it has one or more solutions and inconsistent if no solutions exist.

Answer 2

consistent

Question 3

a consistent system is said to be __________ if it has exactly one solution (often referred to as the unique solution)

Answer 3

independent

Question 4

a consistent system is said to be ___________ if it has more than one
solution. Two systems of equations are equivalent if they have the same solution set

Answer 4

dependent

Question 5

In this method, first we choose one of two equations in a system and solve for one variable in terms of the other. (We make a choice that avoids fractions, if possible.) Then we substitute the result into the other equation and solve the resulting linear equation in one variable. Finally, we substitute this result back into the results of the first step to find the second
variable

Answer 5

SUBSTITUTION

Question 6

is probably the most important method of solution. It readily generalizes to larger systems and forms the basis for computer-based solution methods.

Answer 6

ELIMINATION BY ADDITION

Question 7

The following elementary row operations performed on an augmented matrix produce an equivalent augmented matrix:

Answer 7

1. Interchange two rows.
2. Multiply every element in a row by a nonzero real number.
3. Add a multiple of one row to another row

Question 7

The linear system must have:

Answer 7

A. Exactly one solution
or
B. No solution
or
C. Infinitely many solutions.

Question 8

A system of linear equations is transformed into an equivalent system if:

Answer 8

(A) Two equations are interchanged.

(B) An equation is multiplied by a nonzero constant.

(C) A constant multiple of one equation is added to another equation.