Question

Solve the following system of linear equations.3x – 2y +z = 124x – 3y - 5z = 114x + 3y + 3z = - 5-=AnswerX =y =z =

Answer 1

given

3x-2y+z=12 , 4x-3y-5z=11 , 4x+3y+3z=-5

3x-2y+z=12

3x=12-z+2y

x=(12-z+2y)/3 ....................(1)

4x-3y-5z=11

put the value of x in the above equation

4((12-z+2y)/3)-3y-5z=11

48-4z+8y-9y-15z=33

-19z-y=33-48

-19z-y=-15

-y=-15+19z

y=15-19z .....................(2)

4x+3y+3z=-5

put value of x and y in the given equation

`\begin{gathered} 4((12-z+2(15-19z))/(3))+3(15-19z)+3z=-5 \\ 4((12-z+30+38z)/(3))+45-5z+3z=-5 \\ 48-4z+120+152z+135-15z+9z=-15 \end{gathered}`
`303+142z=-15`

142z=288

z=2.02

put the value of z in equation in equation (2)

y=15-19*2.02

y=-23.38

put the value of value of y and z in equation (1)

`\begin{gathered} x=((12-2.02+2*-23.38)/(3)) \\ =(-36.78)/(3) \\ =12.26 \end{gathered}`

x=12.26