Mathematics: 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

=39/5639 over 5639__56 Please Mark As :D...

Use the gauss-jordan method to solve the following

haybaby312oxdjli

05.01.2022

The system $x+y=7\\3x+2y=17$ has a unique solution $x=3\\y=4$

Step-by-step explanation:

We have the system of equations:

$x+y=7\\3x+2y=17$

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

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

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

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

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

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

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

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

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

$x=3\\y=4$

0,0(0 оценок)