Solve the system and write the solution as a vector 1 2 3 18

Solve the system and write the solution as a vector

x+2y-3z= -18 ---------------------(1)

x+5y+3z= 21----------------------(2)

2x+3y+5z=16---------------------(3)

We eliminate one variable at a time

Adding (1) and (2) we get 2x+7y= 3-----------------(4)

5* (2) +3*(3) we get 5x+25y+15z= 105

6x+9y+15z= 48

Subtracting the two equations we get -x+16y =57 or x-16y =-57-------------------------(5)

Now we solve (4) and (5)

2x+7y=3

2x-32y =-114

Subtracting we get 39y= 117 so y =3

x-16y=-57

x- 48=-57

x=-57+48= -9

Now x+2y-3z=-18

-9+2*3 -3z=-18

-9+6-3z=-18

-3-3z=-18

3+3z=18

3z=18-3=15

z=5

the solution is (-9,3,5)