Question

Linear equations in replacement method2x + 2y − z = 04y − z = 1−x − 2y + z = 2

Answer 1

The given system is:

`\begin{gathered} 2x+2y-z=0\ldots(i) \\ 4y-z=1\ldots(ii) \\ -x-2y+z=2\ldots(iii) \end{gathered}`

Multiply (iii) by 2 to get:

`-2x-4y+2z=4\ldots(iv)`

Add (i) and (iv) to get:

`\begin{gathered} 2x+2y-z=0 \\ + \\ -2x-4y+2z=4 \\ -2y+z=4\ldots(v) \end{gathered}`

Add (ii) and (v) to get:

`\begin{gathered} 4y-z=1 \\ + \\ -2y+z=4 \\ 2y=5 \\ y=(5)/(2) \end{gathered}`

Put y=5/2 in (ii) to get:

`\begin{gathered} 4((5)/(2))-z=1 \\ 10-z=1 \\ -z=-9 \\ z=9 \end{gathered}`

Put y=5/2 and z=9 in (i) to get:

`\begin{gathered} 2x+2((5)/(2))-9=0 \\ 2x+5-9=0 \\ 2x-4=0 \\ 2x=4 \\ x=2 \end{gathered}`

So the values are x=2,y=5/2 and z=9.