Question 931172
<pre>
x+y+z+w=30
5x+10y+25z+50w=645
y=2z
w=x+2

Substitute 2z fo y and x+2 for w in the first two equations:

x+2z+z+x+2=30      5x+10(2z)+25z+50(x+2)=645

Simplify

2x+3z+2=30         5x+20z+25z+50x+100=645
  2x+3z=28                55x+45z+100=645
                              55x+45z=545
                               11x+9z=109

     

So we have the system:

  2x+3z=28
 11x+9z=109

Multiply the top equation by -3 and add the bottom equation:

 -6x-9z=-84
 11x+9z=109
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  5x   = 25
      x=5

You finish:

x = 5, y = 12, z = 6, w=7

Edwin</pre>