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Solve the following system of equations:

 May 25, 2019
 #1
avatar+19326 
+1

START this way:

Multiply FIRST equation by  -2

   then add to equation 3 

      this will allow you to solve for z...........continue on your own and see if you can find x and y

 May 25, 2019
 #2
avatar+104069 
+1

First....there is no "set" way of doing this.....using EP's  idea we have 

 

-2x + 2y - 6z  = -12

2x -  2y + 5z  = 9          add these  and we get

 

-z  = -3

z = 3

 

Now using the first equation we have that 

x - y +  3(3) = 6

x - y + 9  = 6        subtract 9 from both sides

x - y  = -3    

 

So now we have two equations to work with

 

x - y  = - 3     multiply through by - 1   ⇒   -x + y  = 3      (4)

x - 2y  = 5       (5)

 

Add  (4)  and (5)  and we have that

 

-y = 8   ⇒    y  = - 8

 

And using (4) to find x   -x + (-8) = 3       add 8 to both sides

 

-x = 11

x = -11

 

So

 

{x, y, z}  = { -11, -8, 3 }

 

These take some real practice, GM.......also......easy to make mistakes.....be careful !!!

 

 

cool cool cool

 May 25, 2019

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