Solve frac{9/4u_{1}-u_{1}}{9/4u_{1}-u_{2}}=frac{4u_{1}}{u_{2}}

$$\frac { \frac { 9 } { 4 } u _ { 1 } - u _ { 1 } } { \frac { 9 } { 4 } u _ { 1 } - u _ { 2 } } = \frac { 4 u _ { 1 } } { u _ { 2 } }$$

Solve for u_1

$$u_{1}=\frac{7u_{2}}{12}$$

$$u_{1}=0\text{, }u_{2}\neq 0$$

Solve for u_2

$$\left\{\begin{matrix}u_{2}=\frac{12u_{1}}{7}\text{, }&u_{1}\neq 0\\u_{2}\neq 0\text{, }&u_{1}=0\end{matrix}\right.$$