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2.) Solve the system of equations:

x - y - z = 0

2x + 3y + z = 17

z + 2y = 7

 Feb 10, 2019
 #1
avatar+101856 
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x - y - z = 0

2x + 3y + z = 17

z + 2y = 7

 

No set way to do this GM.....but here is an approach....the idea is to get to two equations and two unknowns

Using the 3rd equation.....we can write    z = 7 - 2y

 

Sub this into the first two equations for z

 

x - y - [ 7 - 2y ]  =  0     ⇒    x - y - 7 + 2y = 0   ⇒    x + y    = 7     (4)

2x + 3y + [ 7 - 2y ] = 17 ⇒   2x + y  + 7 = 17 ⇒    2x + y = 10      (5)

 

We can rewrite (4)  as  y = 7 - x

Sub this into (5)

 

2x + ( 7 - x) = 0

x + 7 = 10

x = 3

 

So...y =  7 - x =   7 - 3  = 4

 

And

z = 7 - 2(y)   =  7 - 2(4)  = - 1

 

So   { x, y, z }      =      { 3, 4 , -1 }

 

 

cool cool cool

 Feb 10, 2019

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