Find the solution for these systems of equations

2x+3y=-7

4x-3y=-23

If we add these two equations together, we can quickly follow the system via the elimination method as the y-terms cancel out. Doing so results in 6x = - 30, so x = - 5. Plug this in and solve for y. 2 * (-5) + 3y = - 7, - 10 + 3y = - 7, 3y = 3, y = 1. The solution is therefore (-5,1).