Answer
$r=5.3\Omega$
$E=11V$
Work Step by Step
$I_1r+V_1=E$
$\frac{V_1}{R_1}r+V_1=E$
$\frac{9.7V}{35\Omega}r+9.7V=E$
$I_2r+V_2=E$
$\frac{V_2}{R_2}r+V_2=E$
$\frac{8.1V}{14\Omega}r+8.1V=E$
$\frac{9.7V}{35\Omega}r+9.7V=E$
$r=5.3\Omega$
$E=11V$