Solving equations with 3 unknowns I have the following $3$ equations:
$$\begin{align} A_0 + A_1 + A_2 &= 2 \\ \frac{1}{2}A_1 + A_2 &= 2 \\ \frac{1}{4}A_1 + A_2 &= \frac{8}{3} \end{align}$$
What is the process of solving this? I'm pretty sure $A_0 = A_2$. I'm just confused how to get started. Suggestions?

Simple way: solve for $A_1$ in terms of $A_2$ using the third equation, then solve for $A_2$ using the second. You now have values for $A_1$ and $A_2$. Then, solve for $A_0$.
Alternatively, set it up as a matrix-vector equation, and solve using linear algebra:
$$\begin{pmatrix} 1 & 1 & 1 \\ 0 & \frac12 & 1 \\ 0 & \frac14 & 1 \end{pmatrix}\begin{pmatrix} A_0 \\ A_1 \\ A_2 \end{pmatrix}  = \begin{pmatrix} 2 \\ 2 \\ \frac{8}{3}\end{pmatrix}$$
