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: \[ \begin{cases} 2x + y = 1 \quad \text{(Equation 1)} \\ 2x + 3y = 12 \quad \text{(Equation 2)} \end{cases} \] We'll use the **elimination method** to find the values of \( x \) and \( y \). ### Step 1: Subtract Equation 1 from Equation 2 \[ \begin{align*} (2x + 3y) - (2x + y) &= 12 - 1 \\ 2x + 3y - 2x - y &= 11 \\ (2x - 2x) + (3y - y) &= 11 \\ 2y &= 11 \\ y &= \frac{11}{2} \end{align*} \] ### Step 2: Substitute \( y = \frac{11}{2} \) into Equation 1 \[ \begin{align*} 2x + y &= 1 \\ 2x + \frac{11}{2} &= 1 \\ 2x &= 1 - \frac{11}{2} \\ 2x &= \frac{2}{2} - \frac{11}{2} \\ 2x &= -\frac{9}{2} \\ x &= -\frac{9}{4} \end{align*} \] ### Solution \[ x = -\frac{9}{4} \quad \text{and} \quad y = \frac{11}{2} \] **Alternatively, in decimal form:** \[ x = -2.25 \quad \text{and} \quad y = 5.5 \]