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Decide Model on Cereal

Autor:   •  July 17, 2019  •  Essay  •  408 Words (2 Pages)  •  33 Views

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Algebra 2

Writing Assignment: Systems of Equations

Each problem is worth 5 Points

Total Points: 50

 

Solve each system of equations. Show your work.  

 

  1. -2x + 3y = 8

     3x – y = -5

 

 The equations are

3y=8+2x

and

y=3x+5

Multiplying the second equation by 3

3y=9x+15

Therefore,

8+2x=9x+15

Solving for x

7x=−7

x=−1

and

y=3x+5=3−1+5=2

The solutions are (-1,2)

 

 

  1. 4x - y = 8  

   -8x + 2y = -5

 

 The equations are

y=4x−8

and

2y=8x−5

Multiplying the first equation by 2

2y=8x−16

Therefore

8x−5=8x−16

−5=−16

There are no solutions and the system is inconsistent.

 

 

  1. 5x + y = 13

    3x = 15 – 3y

 

 The equations are

y=−5x+13

and

3y=15−3x

Dividing the last equation by 3

y=5−3x

Therefore,

−5x+13=5−3x

Solving for x

2x=13−5=8

x=2

and

y=−52+13=3

The system is consistent and has one solution (2,3)

 

 

  1. 2x + 4y = 36

    10y = 5

 

 The equations are

2x=36−4y

x=18−2y

and

10y=5

y=2

and

x=18−22=18−4=14

The system is consistent and has one solution (14,2)

 

  1. 2x – 4y = 12     3x – 6y = 21

 

 The equations are

2x=4y+12

That is

x=2y+6

and

3x=6y+21

That is

x=2y+7

Therefore,

2y+6=2y+7

6=7

The system has no solutions and is inconsistent.

 

 

  1. 2x – 9y = 32

    4x + y = -12

...

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