This paper deals with an integral equation technique to reduce the solution of $n(n\geqq 2)$ simultaneous Fredholm integral equations of the first kind to that of $2n$ Volterra integral equations of the first kind and n simultaneous Fredholm integral equations of the second kind. The $2n$ Volterra integral equations of the first kind have a simple kernel and can, therefore, be easily inverted, while the n Fredholm integral equations of the second kind can be easily solved by the standard iterative procedure. The technique is further illustrated by solving two boundary value problems in electrostatics and diffraction theory.