Answer
$$w =b_{3} $$ $$ v= b_{2}- b_{3}$$ $$u= b_{1}+ b_{2}$$
Work Step by Step
Given
$$\begin{aligned} u-v-w &=b_{1} \\ v+w &=b_{2} \\ w &=b_{3} \end{aligned}$$
So, we have $$w =b_{3} $$
Since we have $$ v+w =b_{2}\\ \Rightarrow v=b_{2}-w= b_{2}- b_{3}$$
Also $$ u-v-w =b_{1}\\ \Rightarrow u=b_{1}+v+w= b_{1}+ b_{2}- b_{3}+ b_{3}\\
\Rightarrow u= b_{1}+ b_{2}$$