\(x-y=-9\\ y-z=-10\\ z+x=11\\ \left(x-y\right)+\left(y-z\right)=\left(-9\right)+\left(-10\right)\\ x-y+y-z=-19\\ x-z=-19\\ \left(x-z\right)+\left(z+x\right)=\left(-19\right)+11\\ x-z+z+x=-8\\ 2x=-8\\ x=-8:2\\ x=-4\\ x-y=-9\\ -4-y=-9\\ y=-4-\left(-9\right)\\ y=5\\ z+x=11\\ z+\left(-4\right)=11\\ z=11-\left(-4\right)\\ z=15\)