<PRE><B>Question 936830</B>

This is a 3 variable linear equation problem, that I am not sure how to combine to solve. The problem is to solve the system using linear combination method. Here are the three equations:

5x-4y+4z=18
-x+3y-2z=0
4x-2y+7z=3

I have combined the first and second problem to eliminate z, but I don&#39;t know what to do from there. 

First I distibuted a scale of 2 to the second problem so that the z&#39;s would cancel out, and then I solved. 

(2)-x+3y-2z=0
-2x+6y-4z=0

    5x-4y+4z=18
+  -2x+6y-4z=0
__________________
    3x+2y   =18
Please help me eliminate another variable so I can solve the rest of the problem.
&lt;pre&gt;&lt;font face = &quot;Tohoma&quot; size = 4 color = &quot;indigo&quot;&gt;&lt;b&gt;The easiest variable to eliminate is x. You do this by MULTIPLYING equation 2 by 5 to create equation (iv).
Then subtract equation (iv) from equation (i). You now have an equation in 2 unknowns (y and z). This is equation (v)

You then MULTIPLY equation 2 by 4 to create equation (vi). Then subtract equation (vi) from equation (iii).
You now have an equation in 2 unknowns (y and z). This is equation (vii)

Eliminate one of the variables from equations (v) and (vii). When you have 1 equation in 1 unknown,
and solve for that unknown, you will then be able to determine the values for the other 2 variables. 

When all is &quot;said and done,&quot; you should obtain: {{{highlight_green(system(x = 6,	y = 0_and,z = - 3))}}}
You can do the check!! 
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If you need a complete and detailed solution, let me know!!
&lt;/font face = &quot;Tohoma&quot; size = 4 color = &quot;indigo&quot;&gt;&lt;/b&gt;Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com.
Further help is available, online or in-person, for a fee, obviously. 

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