In this paper the simultaneous distributed consensus and fault-tolerance controls of linear multi-agent systems utilizing edge dynamics are proposed. We show that based on the edge dynamics, the effects of faults and disturbances on the state consensus are eliminated, and the edge dynamics with the proposed algorithms are asymptotically stable under the assumption that the matching conditions hold. A lower-order state observer is designed belonging to the edge dynamics, and the states of the observer are prevented from becoming infinite, which can reduce the burden on the actuators. Finally, a numerical simulation example is given to illustrate the effectiveness of the proposed methods.