Question

Solve.x - 2y + 32 = 83y +z = 12-2x + 2z=-4

Answer 1

Step 1: Write out the equations and label them

`\begin{gathered} x-2y+32=8 \\ \text{ therefore} \\ x-2y=8-32=-24 \\ x-2y=-24-------(1) \end{gathered}`
`\begin{gathered} 3y+z=12------(2) \\ \end{gathered}`
`-2x+2z=-4------------------(3)`

Step 2: From equation (1) we make isolate x to get equation (4)

`x=2y-24--------------(4)`

Step 3: Substitute equation (4) into equation (3)

`\begin{gathered} -2(2y-24)+2z=-4 \\ \text{ Therefore} \\ 2y-24-z=2 \\ 2y-z=26----------(5) \end{gathered}`

Step 4: Add equation (5) to equation (2)

`\begin{gathered} 2y-z=26----------(5) \\ + \\ 3y+z=12------(2) \\ --------------------- \\ 5y=38 \\ y=(38)/(5) \end{gathered}`

Step 5: Substitute the value o f y = 38/5 into equation (5)

`\begin{gathered} 2((38)/(5))-z=26 \\ z=-(54)/(5) \end{gathered}`

Step 6: Substitute the value of y = 38/5 into equation (1)

`\begin{gathered} x-2((38)/(5))=-24 \\ x=-(44)/(5) \end{gathered}`

Hence, the solution is given by

x = -8.8, y = 7.6, and z = -10.8

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