## 4. Solve the system of equations

$$
\left\{\begin{array}{l}
x+y+z=1 \\
a x+b y+c z=d \\
a^{2} x+b^{2} y+c^{2} z=d^{2}
\end{array}\right.
$$

where $a, b, c$ are real parameters such that $a \neq b \neq c \neq a$.
Solution. Under the given conditions, the system has a unique solution

$$
x=\frac{(d-b)(d-c)}{(a-b)(a-c)}, \quad y=\frac{(d-a)(d-c)}{(b-a)(b-c)}, \quad z=\frac{(d-a)(d-b)}{(c-a)(c-b)}
$$