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Solve the system by elimination:

2x - y + 5z = 28

2x - 10y - 5z = 6

x + 5y - 4z = -23

 Dec 11, 2020
 #1
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2x - y + 5z = 28     (1)

2x - 10y - 5z = 6   (2)

x + 5y - 4z = -23     (3)

 

Multiply first equation by -10

-20x + 10y - 50z  = -280

Add this to  (2)  and we  get

-18x - 55z  = -274   (4)

 

Multiply the last equation  by 2

2x  + 10y - 8z  = -46 (5)

Add this to(2)  and we get

4x -13z = -40  (5)

 

Using (4)  and (5)

-18x - 55z  = -274                 multiply  by 4

4x - 13z  =  -40                     multiply by 18

 

-72x - 220z = -1096

72x -234 z  = -720         add these

 

- 454z =  1816    divide both sides  by  -454

z  = 4

 

And

4x - 13(4)  = -40

4x -52  =  -40

4x = 52-40

4x = 12

x  = 3

 

And

2(3) - y  + 5(4)  = 28

12-y + 20 =  28

32 - y = 28

y  = 4

 

{ x, y, z}  = { 3, 4, 4}

 

 

cool cool cool

 Dec 11, 2020

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