Abstract In this article, we solve the system of additive functional equations: <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="block"> <m:mfenced open="{" close=""> <m:mrow> <m:mspace depth="1.25em" /> <m:mtable displaystyle="true"> <m:mtr> <m:mtd columnalign="left"> <m:mn>2</m:mn> <m:mi>f</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo>+</m:mo> <m:mi>y</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>−</m:mo> <m:mi>g</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>=</m:mo> <m:mi>g</m:mi> <m:mrow> <m:mrow> <m:mo>(</m:mo> </m:mrow> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>,</m:mo> </m:mtd> </m:mtr> <m:mtr> <m:mtd columnalign="left"> <m:mi>g</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo>+</m:mo> <m:mi>y</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>−</m:mo> <m:mn>2</m:mn> <m:mi>f</m:mi> <m:mrow> <m:mrow> <m:mo>(</m:mo> </m:mrow> <m:mrow> <m:mi>y</m:mi> <m:mo>−</m:mo> <m:mi>x</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>=</m:mo> <m:mn>4</m:mn> <m:mi>f</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mtd> </m:mtr> </m:mtable> </m:mrow> </m:mfenced> </m:math> \left\{\phantom{\rule[-1.25em]{}{0ex}}\begin{array}{l}2f\left(x+y)-g\left(x)=g(y),\\ g\left(x+y)-2f(y-x)=4f\left(x)\end{array}\right. and prove the Hyers-Ulam stability of the system of additive functional equations in complex Banach spaces. Furthermore, we prove the Hyers-Ulam stability of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>f</m:mi> </m:math> f -hom-ders in Banach algebras.