From the second equation, z=-2-3x-4y.
Substitute for z in the other two equations:
11x+15y+5(-2-3x-4y)=1,
7x+13y+3(-2-3x-4y)=3.
Simplifying these two equations:
11x+15y-10-15x-20y=1⇒-4x-5y=11,
7x+13y-6-9x-12y=3⇒-2x+y=9.
Multiply the equation above by -2 on each side:
4x-2y=-18 and add to the other equation:
-4x-5y=11
-7y=-7, y=1.
Substituting for y in -2x+y=9:
-2x+1=9, -2x=8, x=-4.
Finally, z=-2-3x-4y=-2+12-4=6.
So the solution is x=-4, y=1, z=6.