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Question

solve the system y =-2x+1/3,3x-2y=8

solve the system -x+3y+2z=5,3x+2y+z=-1,2x-y+3z=4

The table shows an end of the year inventory report for a warehouse stocks two models of cordless telephones, one valued $67 and the other at $100,how many of each model of phone did the warehouse have at the time of the inventory?

Cordless phone 360 $29,400

Answer 1

The system of equations

y =-2x+1/3             ...... (1)

3x-2y=8                  ...... (2)

Substitute -2x+1/3  for y in equation (2).

3x-2(-2x+1/3)=8 

Apply distributive property: a(b + c) = ab + ac

3x-2(-2x) - 2(1/3)=8 

3x + 4x - 2/3=8 

7x - 2/3=8 

Add 2/3 to each side.

7x - 2/3 + 2/3=8 + 2/3

7x = 26/3

Divide each side by 7.

x = 26/21

 

Calculate the value of y:

Substitute 26/21  for x in equation (1).

y =-2x+1/3

y =-2(26/21)+1/3

   =- 52/21+1/3

   = (- 52 + 7)/21

   = - 45/21

   = - 15/7

Answer 2

2)

Given equations

- x + 3y + 2z = 5                ---------------------(1)

3x + 2y + z = -1                 ---------------------(2)

2x -  y + 3z = 4                  ---------------------(3)

(1)   ⇒    - x + 3y + 2z = 5 

3y + 2z = 5 + x

x = 3y + 2z – 5                         ---------------------(4)

Substitute equation (4) in equation (2)

3(3y + 2z – 5) + 2y + z = -1

9y + 6z – 15 + 2y + z = -1

11y + 7z  = -1+15

11y + 7z  = 14                           ---------------------(5)

Substitute equation (4) in equation (3)

2(3y + 2z – 5) -  y + 3z = 4

6y + 4z – 10 -  y + 3z = 4

5y + 7z = 4 + 10

7z = 14 – 5y                              ---------------------(6)

Substitute equation (6) in equation (5)

11y + (14 – 5y)  = 14

6y = 14 – 14

6y = 0

y = 0.

Substitute y = 0 in equation (6)

7z = 14 – 5(0)

z = 14/7

z = 2.

Substitute y = 0 , z = 2 in equation (4)

x = 3(0) + 2(2) – 5

x = 4 – 5

x = - 1.

Solution :

x = - 1 , y = 0 , z = 2.

Answer 3

3)

Let

x = The number of cordless telephones valued $ 67.

y = The number of cordless telephones valued $ 100.

Total number of Cordless phone at end of the year inventory report = x + y

Actual total number of Cordless phone = 360.

x + y = 360

y = 360 - x.                                         --------------------------------- (1)

Merchandise value of cordless telephones valued $ 67 = 67x

Merchandise value of cordless telephones valued $ 100 = 100y

Total Merchandise value of cordless telephones = 67x + 100y

Actual Total Merchandise value of cordless telephones = 29400

67x + 100y = 29400.                            --------------------------------- (2)

Substitute equation (1) in equation (2)

67x + 100(360 - x) = 29400

67x + 36000 - 100x = 29400

36000 - 33x = 29400

36000 – 29400 = 33x

33x = 6600

x = 6600/33

x = 200.

Substitute x = 200 in equation (1)

y = 360 – 200

y = 160

Solution :

The number of cordless telephones valued $ 67 is 200.

The number of cordless telephones valued $ 100 is 160.