System of equations

the following system of equations is shown below. 2x+3y=4 x - y = -3 which of the below is the solution to this system? A) (-13,10) B) (-1,2) C) (1,-2) D) (2,3)

\(\small{ \begin{array}{lrcll} (1) & 2x+3y &=& 4 \qquad & | \qquad -2x\\ & 3y &=& 4-2x \qquad & | \qquad :3\\ & y &=& \frac43-\frac23x \\\\ (2) & x - y &=& -3 \qquad & | \qquad \cdot (-1)\\ & -x + y &=& 3 \qquad & | \qquad +x\\ & y &=& 3+x \\ \hline \\ (2) = (1) \\ & y = 3+x &=& \frac43-\frac23x \\ & 3+x &=& \frac43-\frac23x \qquad & | \qquad +\frac23x\\ & 3+x+\frac23x &=& \frac43 \qquad & | \qquad -3\\ & x+\frac23x &=& \frac43 -3\\ & \frac33x+\frac23x &=& \frac43 -\frac33\cdot 3\\ & \frac33x+\frac23x &=& \frac43 -\frac93\\ & \frac53x &=& -\frac53 \qquad & | \qquad \cdot 3\\ & 5x &=& -5 \qquad & | \qquad :5\\ & x &=& -\frac55 \\ & \mathbf{ x } & \mathbf{=} & \mathbf{-1} \\\\ & y &=& 3+x \\ & y &=& 3-1 \\ & \mathbf{ y } & \mathbf{=} & \mathbf{2} \\\\ \end{array} }\)

B) (-1,2) is the answer