Use backsubstitution to solve the triangular system 2x y 4

Use back-substitution to solve the triangular system. {2x - y + 4z = 3 y + 3z = 0 -2z = 1 (x, y) = ()

Solution

2x - y +3z = 3

y +2z =0

-2z = 1

So, we have z = -1/2

substituting in equation 2:

y -1 =0 ; y = 1

Now substitute value of y and z in equation 1 :

2x - 1 +4(-1/2) =3

2x - 1 - 2 =3

2x = 6

x = 2

(x , y z ) = ( 2 , 1 , -1/2)