Solve I=frac{E_{g}}{R_{L}+R_{j}}=500/10+1000=0.495A

$$I = \frac { E _ { g } } { R _ { L } + R _ { j } } = \frac { 500 } { 10 + 1000 } = 0.495 A$$

Evaluate (complex solution)

$$I=\frac{E_{g}}{R_{L}+R_{j}}\text{ and }\frac{E_{g}}{R_{L}+R_{j}}=\frac{50}{101}\text{ and }A=\frac{10000}{9999}$$

Solve for R_j

$$R_{j}=\frac{101E_{g}}{50}-R_{L}$$

$$I=\frac{50}{101}\text{ and }A=\frac{10000}{9999}\text{ and }E_{g}\neq 0$$

Solve for R_L

$$R_{L}=\frac{101E_{g}}{50}-R_{j}$$

$$I=\frac{50}{101}\text{ and }A=\frac{10000}{9999}\text{ and }E_{g}\neq 0$$