Solution SSLE.C30 Chris Black

Solving each equation for $y$, we have the equivalent system \begin{align*} y &= 5 - x\\ y &= 2x - 3. \end{align*} Setting these expressions for $y$ equal, we have the equation $5 - x = 2x - 3$, which quickly leads to $x = \frac{8}{3}$. Substituting for $x$ in the first equation, we have $y = 5 - x = 5 - \frac{8}{3} = \frac{7}{3}$. Thus, the solution is $x = \frac{8}{3}$, $y = \frac{7}{3}$.