**Solution to Linear Algebra Hoffman & Kunze Chapter 1.2 Exercise 1.2.2**

Solution: Yes the two systems are equivalent. We show this by writing each equation of the first system in terms of the second, and conversely.

\begin{alignat*}{2}

3x_1+x_2&=\frac13(x_1-x_2)+\frac43(2x_1+x_2)\\

x_1+x_2 &= \frac{-1}3(x_1-x_2)+\frac23(2x_1+x_2)\\

x_1-x_2 &= (3x_1+x_2)-2(x_1+x_2)\\

2x_1+x_2&=\frac12(3x_1+x_2)+\frac12(x_1+x_2)

\end{alignat*}