Question

Linear equation in deletion method2x + y − 3z = 13x − y − 4z = 75x + 2y − 6z = 5

Answer 1

The given system is:

`\begin{gathered} 2x+y-3z=1\ldots(i) \\ 3x-y-4z=7\ldots(ii) \\ 5x+2y-6z=5\ldots(iii) \end{gathered}`

Add (i) and (ii) to get:

`\begin{gathered} 2x+y-3z=1 \\ + \\ 3x-y-4z=7 \\ 5x-7z=8\ldots(iv) \end{gathered}`

Multiply (ii) by 2 to get:

`6x-2y-8z=14\ldots(v)`

Add (iii) and (v) to get:

`\begin{gathered} 6x-2y-8z=14 \\ + \\ 5x+2y-6z=5 \\ 11x-14z=19\ldots(vi) \end{gathered}`

Multiply (iv) by 2 to get:

`10x-14z=16\ldots(vii)`

Subtract (vii) from (vi) to get:

`\begin{gathered} 11x-14z=19 \\ - \\ 10x-14z=16 \\ x=3 \end{gathered}`

Put x=3 in (iv) to get:

`\begin{gathered} 5*3-7z=8 \\ -7z=8-15 \\ -7z=-7 \\ z=1 \end{gathered}`

Put x=3 and z=1 in (i) to get:

`\begin{gathered} 2(3)+y-3(1)=1 \\ 6+y-3=1 \\ y+3=1 \\ y=-2 \end{gathered}`

So the values are x=3,y=-2 and z=1.