\( \begin{array}{l}x-2 y=3 \\ 5 x+3 y=2\end{array} \) The lines whose equations are shown intersect at which point? \( (1,-1) \) \( (0,312) \) \( (-1,1) \)

To find the intersection point of the two lines represented by the equations \(x - 2y = 3\) and \(5x + 3y = 2\), we can solve this system of equations. First, rewrite the first equation to express \(x\) in terms of \(y\): \[ x = 2y + 3. \] Now, substitute \(x\) in the second equation: \[ 5(2y + 3) + 3y = 2. \] Distributing gives: \[ 10y + 15 + 3y = 2. \] Combining like terms: \[ 13y + 15 = 2. \] Now, solve for \(y\): \[ 13y = 2 - 15 \] \[ 13y = -13 \] \[ y = -1. \] Now substitute \(y = -1\) back into the equation \(x = 2y + 3\): \[ x = 2(-1) + 3 = -2 + 3 = 1. \] Thus, the lines intersect at the point \((1, -1)\).