Solve the system with the addition method: \[ \left\{\begin{array}{l} 5 x+2 y=-4 \\ -6 x-5 y=3 \end{array}\right. \] Answer: Enter your answers as integers or as reduced fraction(s) in the form A/B. Check Answer

Step 1 ：Given the system of equations: \[\left\{\begin{array}{l} 5x+2y=-4 \\ -6x-5y=3 \end{array}\right.\]

Step 2 ：First, we multiply the first equation by 5 and the second equation by 2 to make the coefficients of y the same in both equations. This gives us: \[\left\{\begin{array}{l} 25x+10y=-20 \\ -12x-10y=6 \end{array}\right.\]

Step 3 ：Next, we add the two equations together to eliminate y. This gives us: \[13x=-14\]

Step 4 ：Solving for x, we get: \[x=-\frac{14}{13}\]

Step 5 ：Substituting \(x=-\frac{14}{13}\) into the first equation, we can solve for y: \[y=\frac{9}{13}\]

Step 6 ：Final Answer: The solution to the system of equations is \[\boxed{x=-\frac{14}{13}}\] and \[\boxed{y=\frac{9}{13}}\]