Tax multiplier in IS-LM model
Hint:
The $T$ is variable itself so the total differential should read as:
$$dY = C'dY - C'dT + I'dr + dG \implies dY = \frac{1}{1-C'}I 'dr + \frac{1}{1-C'}dG - \frac{C'}{1-C'}dT$$
Furthermore, by Fisher equation $r=i-\pi$. Hence we have:
$$dY = \frac{1}{1-C'}I 'di - \frac{1}{1-C'}I 'd\pi + \frac{1}{1-C'}dG - \frac{C'}{1-C'}dT$$
$$(1/P)dM - (M/P^2) dP = L_r'dr + L_Y' dY - L_T'dT$$
again use the Fisher so:
$$(1/P)dM - (M/P^2) dP = L_i'di - L_{\pi}'d \pi + L' dY - L'dT$$
This is IS-LM model so you are looking for equilibrium output and nominal interest rate $dY$ and $di$. You have two equations and two unknowns. You can solve it even with substitution but you should probably follow the textbook's advice to use Cramer's rule.