You have three equations and assuming that the x, y, and z all have the same value for all equations. The best way to solve this is to start by rearranging the first equation to isolate X.
X+5y-4z=-10
X=4z-5y-10
Then you do the same with the second equation to isolate y.
2x-Y+5z=-9
2x+5z+9=Y
Substitute the X equation into the second rearranged equation.
2(4z-5y-10)+5z+9=Y
Simplify
8z-10y-20+5z+9=Y
13z-10y-11=Y … 13z-11=11Y … Y=(13z-11)/11
Substitute the X equation into the third equation.
2x-10y-5z=0
2(4z-5y-10)-10Y-5z=0
8z-10y-20-10Y-5z=0
Simplify
3z-20y=20
Insert the Y into the third equation
3z-20(13z-11)/11=20
3z-(260z+220)/11=20
Multiple by 11 & Simplify
33z-260z+220=220 … -227z=0
Divide this out and you will determine that Z =0
Now put your Z value into the Y equation
Y=(13(0)-11)/11
Y=0-11/11
Y=-1
Finally, solve the first equation
X=4z-5y-10
X=4(0)-5(-1)-10
X=0+5-10
X=-5
Your answer is option C … (-5, -1, 0)
