Question

Determine the number of solutions for the following system of linear equations. If there is only onesolution, find the solution.2x + y - 5z = -2- 4x + 4y - 62 = 36x – 3y + z = -7AnswerKeypadKeyboard ShortcutsSelecting an option will enable input for any required text boxes. If the selected option does not have anyassociated text boxes, then no further input is required.O No SolutionO Only One SolutionX=y =%3DO Infinitely Many Solutions

Answer 1

We have the following system of linear equations:

`\begin{gathered} 2x+y-5z=-2, \\ -4x+4y-6z=3, \\ 6x-3y+z=-7. \end{gathered}`

1) We solve for x the first equation:

`\begin{gathered} 2x+y-5z=-2, \\ 2x=5z-y-2, \\ x=(1)/(2)\cdot(5z-y-2)\text{.} \end{gathered}`

2) We replace the last equation in the second and third equations:

`\begin{gathered} -4\cdot(1)/(2)\cdot(5z-y-2)+4y-6z=3, \\ 6\cdot(1)/(2)\cdot(5z-y-2)-3y+z=-7. \end{gathered}`

Simplifying these equations, we have:

`\begin{gathered} 6y-16z+4=3, \\ -6y+16z-6=-7. \end{gathered}`

3) Multiplying by -1 the last equation, we have:

`\begin{gathered} 6y-16z+4=3, \\ 6y-16z+6=7. \end{gathered}`

4) Isolating the term 6y - 16z in each equation, we have:

`\begin{gathered} 6y-16z=-1, \\ 6y-16z=1. \end{gathered}`

5) Equalling the equations, we get:

`-1=1.`

Which is absurd. So we conclude that the system of equations is incompatible and it has no solutions.

Answer: No Solution