UMUC MATH106 Week 3 Discussion Latest 2019 January Question # 00599589 Subject: Education Due on: 03/19/2019 Posted On: 03/19/2019 06:01 AM Tutorials: 1 Rating: 4.7/5

MATH 106
6383 Finite Mathematics (2192)

Week 3
Discussion

AUGMENTED MATRIX METHOD TO
SOLVE SYSTEM OF LINEAR EQUATIONS (Precalculus, Section 9.7)

For
the following exercises, write the augmented matrix for the linear system.

1.
8x?37y=8 2x+12y=3

2.
2x?3y=?95x+4y=58

3.
6x+2y=?43x+4y=?17

4.
2x+3y=12 4x+y=14

For the following
exercises, solve the system by Gaussian elimination.

5.

6.

7.

8.

9.

10.

11.

For
the following exercises, set up the augmented matrix that describes the
situation, and solve for the desired solution.

12.
Every day, a cupcake store sells 5,000 cupcakes in chocolate
and vanilla flavors. If the chocolate flavor is 3 times as popular as the
vanilla flavor, how many of each cupcake sell per day?

13.
At a competing cupcake store, $4,520 worth of cupcakes are
sold daily. The chocolate cupcakes cost $2.25 and the red velvet cupcakes cost
$1.75. If the total number of cupcakes sold per day is 2,200, how many of each
flavor are sold each day?

14.
You invested $10,000 into two accounts: one that has simple
3% interest, the other with 2.5% interest. If your total interest payment after
one year was $283.50, how much was in each account after the year passed?

GRAPHING LINEAR
INEQUALITIES IN TWO VARIABLES (Basic Mathematics Review, Section
7.8)

For the followingexercises,
graph the inequalities and show (shade in) the solution region.

15.
y?x+2

16.
y<?12x+3

17.
2x
+ 3y ? – 6

18.
2x+5y?20

19.
– 4x
+ 3y? 12

20.
3x>– 12

21.
7y? 21

22.
x+4y> 4

GRAPHING SYSTEMS OF
LINEAR INEQUALITIES IN TWO VARIABLES
(UMUC Course Module 1, Topic II)

For the followingexercises,
graph the system of inequalities. Show
(by shading in) the feasible
region.

23.
y? – x+2 , y? – 5x + 2

24.
4x
+ y<2 ,y> – 2

25.
3x
+ 2y ? 2
, x + 2y ? 2

26.
4x+3y> – 9
, 2x – 3y ? – 9

27.
5x + 2y ?
– 4 , x
+ 2y< 4

28.
x
? 0
, y ? 0

For the followingexercises,
graph the system of inequalities. Show
(by shading in) the feasible
region. Identify the ordered-pair
“corner points” that define the feasible region.

29.
3x
+ 2y?10 , 2x
+ 3y
? 10 , x ? 0
, y ? 0

30.
4x
+ y ?16
, x – 3y? – 9
, x ?
0 , y
? 0

31.
4x
+ y ? 8
, x + y ? 5 , x ?
0 , y
? 0

32.
y ?5 , x –y
?0 , x ?
0 , y ? 0

33.
2x + 5y?20
, x ?5 , y ?
5 , x ?
0 , y ? 0

34.
x + y
? 4 , x
+ 2y ? 5 , x ?
0 , y ? 0