2. What is the \( x \) value in the solution for this system of equations? \[ \left\{\begin{array}{c}2 x-y=-5 \\ -3 x-y=-1\end{array}\right. \]

To solve the system of equations, you can use either substitution or elimination. Let's use elimination in this case. First, we'll subtract the first equation from the second equation: \[ (-3x - y) - (2x - y) = -1 - (-5) \] This simplifies to: \[ -5x = 4 \] Now, divide both sides by -5: \[ x = -\frac{4}{5} \] So, the value of \( x \) in the solution for this system of equations is \( -\frac{4}{5} \). For the value of \( y \), you can substitute \( x \) back into one of the original equations. Using \( 2x - y = -5 \): \[ 2(-\frac{4}{5}) - y = -5 \] This simplifies to: \[ -\frac{8}{5} - y = -5 \] To solve for \( y \), first convert -5 to a fraction with a denominator of 5: \[ -\frac{8}{5} - y = -\frac{25}{5} \] Now, add \( \frac{8}{5} \) to both sides: \[ -y = -\frac{25}{5} + \frac{8}{5} \] \[ -y = -\frac{17}{5} \] Thus: \[ y = \frac{17}{5} \] So, the solution to the system of equations is \( x = -\frac{4}{5} \) and \( y = \frac{17}{5} \).