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This paper presents sufficient conditions for the solvability of the third order three point boundary value problem-u′′′(t)=f(t,v(t),v′(t))-v′′′(t)=h(t,u(t),u′(t))u(0)=u′(0)=0,u′(1)=αu′(η)v(0)=v′(0)=0,v′(1)=αv′(η).The arguments apply Green's function associated to the linear problem and the Guo--Krasnosel'skiĭ theorem of compression-expansion cones. The dependence on the first derivatives is overcome by the construction of an adequate cone and suitable conditions of superlinearity/sublinearity near 0 and +∞. Last section contains an example to illustrate the applicability of the theorem

On the Solvability of Third-Order Three Point Systems of Differential Equations with Dependence on the First Derivative