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Use the Gauss-Jordan method to solve the following system of equations x+y 7 3x+2y= 17 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution is (Туре an ordered pair.) O B. There are infinitely many solutions. The solution is y, where y is any real number (Use integers or fractions for any numbers in the expression.) O C. The system is inconsistent

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Answer:

The system [tex]x+y=7\\3x+2y=17[/tex] has a unique solution [tex]x=3\\y=4[/tex]

Step-by-step explanation:

We have the system of equations:

[tex]x+y=7\\3x+2y=17[/tex]

To solve this system for Gauss-Jordan method we need the augmented matrix, which is:

[tex]\left[\begin{array}{cc|c}1&1&7\\3&2&17\end{array}\right][/tex]

Next we need to transform the augmented matrix to the reduced row echelon form via elementary row operations as follows:

  • Row Operation 1: add -3 times the 1st row to the 2nd row

[tex]\left[\begin{array}{cc|c}1&1&7\\0&-1&-4\end{array}\right][/tex]

  • Row Operation 2: multiply the 2nd row by -1

[tex]\left[\begin{array}{cc|c}1&1&7\\0&1&4\end{array}\right][/tex]

  • Row Operation 3: add -1 times the 2nd row to the 1st row

[tex]\left[\begin{array}{cc|c}1&0&3\\0&1&4\end{array}\right][/tex]

From the reduced row echelon form we have the solution of the system

[tex]x=3\\y=4[/tex]

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