Solve equ 3-70 for I1(s), then insert that solution into equ 3-69, call that new equation A1 and it only has I2(s) in it now. Then solve equ 3-71 for I2(s), then insert that into the new equation A1, solving for Eo/Ei.
So the whole deal here is to solve for I1 and I2 simultaneously.
It amounts to multiplying one equation by an appropriate parameter (that does not include the variables), and then adding two equations to create a new equation.
In this example, you can either multiply eqn. 3-70 by (1 + R1 C1 s), then add this new equation to 3-69. Or, divide eqn. 3.69 by (1 + R1 C1 s), then add the new equation to 3-70.