SOLUTION: Solve the following system of equations for the unknown variables. 2x + y = 17 y + z = 6 x – z = 7

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Question 143829: Solve the following system of equations for the unknown variables.
2x + y = 17
y + z = 6
x – z = 7

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the third equation


Solve for z


Go to the 2nd equation


Plug in


Add 7 to both sides


Rearrange the terms


So we now have the system






Let's use substitution to solve this system


Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.




So let's isolate y in the first equation

Start with the first equation


Subtract from both sides


Rearrange the equation


Divide both sides by


Break up the fraction


Reduce



---------------------

Since , we can now replace each in the second equation with to solve for



Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.



Combine like terms on the left side


Subtract 17 from both sides


Combine like terms on the right side


Divide both sides by -1 to isolate x



Divide





So the first part of our answer is:









Since we know that we can plug it into the equation (remember we previously solved for in the first equation).



Start with the equation where was previously isolated.


Plug in


Multiply


Combine like terms




So the second part of our answer is:


Go back to the third equation


Plug in




Subtract 4 from both sides


Combine like terms on the right side


Divide both sides by -1 to isolate z



Divide






So the third part of our answer is:



-----------------Summary------------------------------

So our answers are:

, , and


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