Question 553434
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solve the system of equations using the substitution method
x+z=8
y-z=5
x-y=9
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        Yes,  the substitution method is robust and works perfectly,  as tutor @Theo showed in his post.

        But I will show you even more effective method.



<pre>
Add all the three equations.  Then, after  combining like terms, you will get

    2x = 8 + 5 + 9 = 22.


Hence,  x = 22/2 = 11.


Having it, you find from the first equation

    z = 8 - x = 8 - 11 = -3,


and from the second equation

    y = 5 + z = 5 + (-3) = 2.


<U>ANSWER</U>.  x = 11,  y = 2,  z = -3.
</pre>

Solved.


It is a kind of the Elimination method.


Resume: &nbsp;&nbsp;the Substitution method is good, but sometimes other methods 
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;are more effective than the Substitution method.