Solve the following system in three variables using linear combinations. 3x−2y+z=0 4x+y−3z=−9 9x−2y+2z=20

Answer:The solution of the system of equations isx=2,y=7,z=8Step-by-step explanation:we have3x-2y+z=0isolate the variable zz=2y-3x ------> equation A4x+y-3z=-9 ----> equation B9x-2y+2z=20 ----> equation C                  substitute equation A in equation B and equation C4x+y-3(2y-3x)=-94x+y-6y+9x=-913x-5y=-9 -------> equation D9x-2y+2(2y-3x)=209x-2y+4y-6x=203x+2y=20 ----> equation ESolve the system13x-5y=-9 -------> equation D3x+2y=20 ----> equation EMultiply equation E by 2.5 both sides2.5*(3x+2y)=20*2.57.5x+5y=50 -----> equation FAdds equation D and equation F13x-5y=-97.5x+5y=50------------------13x+7.5x=-9+5020.5x=41x=41/20.5x=2Find the value of ysubstitute the value of x in the equation E3(2)+2y=206+2y=202y=20-62y=14y=7Find the value of zSubstitute the value of x and the value of y in equation Az=2y-3xz=2(7)-3(2)z=14-6z=8thereforeThe solution of the system of equations isx=2,y=7,z=8