Question

solve system by any method elimination, substitution .
{x+y+3z=-4
-x-y-2z=5
2x-z=-3}

Answer 1

x+y+3z=-4----(1)
-x-y-2z=5----(2)
2x-z=-3------(3)

in equation 3
2x-z=-3
2x=-3+z
2x=z-3
x=z-3/2-----(4)

put x in equation 2
-x-y-2z=5
-(z-3/2)-y-2z=5
3-z/2-y-2z=5

Taking L.C.M
3-z-2y-4z=10
3-5z-2y=10
2y=3-10-5z
2y=-7-5z
y=-7-5z/2----(5)

put x and y in equation 1
x+y+3z=-4
z-3/2-7-5z/2+3z=-4
Taking L.C.M
z-3-7-5z+6z=-8
-4z+6z-10=-8
2z=-8+10
2z=2
z=1

put z in equation 4
x=z-3/2
x=1-3/2
x=-1

put z in equation 5
y=-7-5z/2
y=-7-5/2
y=-12/2
y=-6

{x,y,z}={-1,-6,1}