9. Solve the system of equations using the method of your choice. \[ \qquad \begin{array}{l}10 \text {. Solv } \\ \text { method } \\ 2 x+y=1 \\ 2 x+3 y=12\end{array} \]

To solve the system of equations: 1. The first equation is \(2x + y = 1\). We can express \(y\) in terms of \(x\): \[y = 1 - 2x.\] 2. Now substitute this expression for \(y\) in the second equation \(2x + 3y = 12\): \[2x + 3(1 - 2x) = 12.\] 3. Distributing the \(3\): \[2x + 3 - 6x = 12.\] \[-4x + 3 = 12.\] 4. Now, isolate \(x\): \[-4x = 12 - 3.\] \[-4x = 9 \Rightarrow x = -\frac{9}{4}.\] 5. Substitute \(x\) back into the expression for \(y\): \[y = 1 - 2\left(-\frac{9}{4}\right) = 1 + \frac{18}{4} = 1 + \frac{9}{2} = \frac{2}{2} + \frac{9}{2} = \frac{11}{2}.\] The solution to the system of equations is \(x = -\frac{9}{4}\) and \(y = \frac{11}{2}\).