Solve: \( \begin{array}{l}3 x+2 y=23 \\ 2 x-y=6\end{array} \)

To solve the system of equations, we can use the method of substitution or elimination. Let's use elimination here. First, we can manipulate the second equation to express \(y\) in terms of \(x\): \(2x - y = 6\) This simplifies to: \(y = 2x - 6\) Now, we substitute \(y\) into the first equation: \(3x + 2(2x - 6) = 23\) This simplifies to: \(3x + 4x - 12 = 23\) Combining like terms, we get: \(7x - 12 = 23\) Now, add 12 to both sides: \(7x = 35\) Now divide by 7: \(x = 5\) Now that we have \(x\), we can find \(y\) using the equation \(y = 2x - 6\): \(y = 2(5) - 6\) This simplifies to: \(y = 10 - 6\) \(y = 4\) So, the solution to the system of equations is: \((x, y) = (5, 4)\)