Let x = 1st number
Let y = 2nd number
Read the problem and translate into two sets of simultaneous equations, and solve by elimination:
6x + 5y = -9 multiply every term of this equation by 5
5x + 8y = 4 multiply every term of this equation by -6
You now have the following equivalent equations where you can eliminate the terms containing x and solve for y.
30x + 25y = -45
-30x - 48y = -24
0x -23y = -69 (divide both sides by -23)
y = 3 plug in 3 for y in either equation and you will find that x = -4
x = -4
Reread the problem and make sure your two solutions make sense...