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x+y+2z=a , x+z= b and 2x+y+3z=c

Show that in order for this system to have at least one solution, a,b,c must satisfy c=a+b.

Obviously I can add the equations a and b and get c. But I dont know how else to approach showing this. I think the points of x,y,z of c must satisfy both a,b and provide a solution set for both but Im not sure how to prove that. HELP PLEASE~!