The second question. We have:
\(\beta_GV(r_m) = \dfrac{2}{7}V(r_G) + \dfrac{5}{7}cov(r_G,r_H)\)
\(\beta_HV(r_m) = \dfrac{5}{7}V(r_H) + \dfrac{2}{7}cov(r_G,r_H)\)
Now I will leave the first equation as it is and multiply the second by \dfrac{5}{2}
\(\beta_GV(r_m) = \dfrac{2}{7}V(r_G) + \dfrac{5}{7}cov(r_G,r_H)\)
\(\dfrac{5}{2}\beta_HV(r_m) = \dfrac{25}{14}V(r_H) + \dfrac{5}{7}cov(r_G,r_H)\)
Finally, I subtract the second equation from the first. Note how the covariance term disappears
\(\beta_G V(r_m)-\dfrac{5}{2}\beta_H V(r_m) = \dfrac{2}{7} V(r_G)-\dfrac{25}{4} V(r_H)\)