Question

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

Answer 1

Given,

The system of equations are,

`\begin{gathered} 2x+y-3z=1\ldots\ldots\ldots\ldots......\ldots.\mathrm{\cdot}..(1) \\ 3x-y-4z=7\ldots\ldots\ldots\ldots\ldots\ldots\ldots.(2) \\ 5x+2y-6z=5​\ldots\ldots\ldots\ldots\ldots.\ldots\text{.}\mathrm{}(3) \end{gathered}`

Adding equation (1) and (2)

`\begin{gathered} 5x-7z=8\ldots.\ldots\ldots\ldots\ldots\ldots\text{.}(4) \\ 7z=5x-8 \\ x=(7z+8)/(5) \end{gathered}`

Substracting equation (4) from (3)

`\begin{gathered} 5x+2y-6z-5x+7z=5-8 \\ 2y+z=-3 \\ y=(-z-3)/(2) \end{gathered}`

Substituting the value of x and y then,

`\begin{gathered} 2x+y-3z=1 \\ 2((7z+8)/(5))+((-z-3)/(2))-3z=1 \\ (14z+16)/(5)-(z-3)/(2)-3z=1 \\ (28z+32-5z-15-30z)/(10)=1 \\ (-7z+17)/(10)=1 \\ -7z=10-17 \\ z=1 \end{gathered}`

Substituting the value of z to get the value of x and y,

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

Hence, the value of x is 3, y is -2 and z is 1.