Question 938340
Four equations, linear, in four unknown variables.  


Your chart is confusing and not just like the description, so the equations could be:


w+x=11
y+z=18
w+y=21
x+z=17


The description does not indicate negative constants.


Substitution throughout could work, but you might want to uses elementary row operations for the equations in a form,  aw+bx+cy+dz=k,  for the variables w, x, y, z.


{{{z=17-x}}}
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{{{y+17-x=18}}},{{{y-x=1}}}
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Newer system
{{{system(w+x=11,-x+y=1,w+y=21)}}}


Take that middle equation, and use {{{y=x+1}}}.
{{{system(w+x=11,w+x+1=21)}}}
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Contradictory, w+x=11 and w+x=20, cannot be!