Solve the system of equations 5 x y z3 226 5x y z9 Solutio

Solve the system of equations. 5) x+ y+ z=3 +22=6 5x + y + z=-9

x+y+z=3...(i)
x-y+2z=6...(ii)
5x+y+z=-9...(i)

solve (i) for x
x=3-y-z...(iv)

plug (iv) into (ii)
x-y+2z=6
3-y-z-y+2z=6
3-2y+z=6
z=3+2y...(v)

plug (iv) into (iii)
5x+y+z=-9
5(3-y-z)+y+z=-9
15-5y-5z+y+z=-9
-4y-4z=-24
y+z=6
y+(3+2y)=6 (from (v) )
y+3+2y=6
3y=3
y=1

plug y=1 into (v)
z=3+2y=3+2*1=5

plug values of y and z into (iv)
x=3-y-z
x=3-1-5
x=-3

Hence the final answer is x=-3, y=1, z=5