Question

Determine the number of solutions for the following system of linear equations. If there is only onesolution, find the solution.- 3x + 6y - 3z = 55x - 5y – 2z = 44x - 3y - 3z = -3AnswerKeypadKeyboard 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 =Jy=02 =O Infinitely Many Solutions

Answer 1

The first step to solve the system of equation is to solve one of the equations for one variable:

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

Replace this variable for the obtained expression in the other two equations:

`\begin{gathered} 5(2y-z-(5)/(3))-5y-2z=4 \\ 4(2y-z-(5)/(3))-3y-3z=-3 \end{gathered}`

Now, solve the system just as if it were a 2x2 system:

`\begin{gathered} 10y-5z-(25)/(3)-5y-2z=4 \\ 5y-7z-(25)/(3)=4 \\ 5y-7z=4+(25)/(3) \\ 5y-7z=(37)/(3) \\ y=(37)/(15)+(7)/(5)z \end{gathered}`
`\begin{gathered} 8y-4z-(20)/(3)-3y-3z=-3 \\ 5y-7z=(20)/(3)-3 \\ 5y-7z=(11)/(3) \\ y=(11)/(15)+(7)/(5)z \end{gathered}`

Make both expressions for y equal and solve for z:

`\begin{gathered} (37)/(15)+(7)/(5)z=(11)/(15)+(7)/(5)z \\ (7)/(5)z-(7)/(5)z=(11)/(15)-(37)/(15) \\ 0=(26)/(15) \end{gathered}`

Since 0 is not equal to 26/15, we can determine that this system does not have any solution.

The correct answer is No solution.