\( 2 x-y=-3 \) and \( 3 x+2 y=8 \)

To solve the system of equations, let’s express both equations clearly. The first equation is \( 2x - y = -3 \), which can be rearranged to find \( y = 2x + 3 \). The second equation is \( 3x + 2y = 8 \). By substituting \( y \) from the first equation into the second, we get \( 3x + 2(2x + 3) = 8 \). Expanding that gives \( 3x + 4x + 6 = 8 \), simplifying to \( 7x + 6 = 8 \). Thus, \( 7x = 2 \), leading to \( x = \frac{2}{7} \). Now, substituting \( x = \frac{2}{7} \) back into the equation \( y = 2x + 3 \) gives us \( y = \frac{4}{7} + 3 = \frac{4}{7} + \frac{21}{7} = \frac{25}{7} \). So, the solution is \( x = \frac{2}{7} \) and \( y = \frac{25}{7} \). Next time you find yourself dealing with equations, consider using substitution or elimination methods to make it easier, as they help avoid mistakes like miscalculating variables. Also, remember to double-check your work by plugging the values back into both original equations to confirm they truly satisfy the equations.