Question

Pivot the system about the element in row 2, column 1. (Enter the augmented matrix with all cells in their original position.)

Answer 1

Answer:

We have the system

$3x+3y=6\\4x+3y=5$

The augmented matrix of the system is

$A=\left[\begin{array}{ccc}3&3&6\\4&3&5\end{array}\right]$

Pivot the system means to use row operations for find the echelon form of the augmented matrix.

Then,

1. In the second row of A we subtract 4/3 from the first row. We obtain:

$B=\left[\begin{array}{ccc}3&3&6\\0&-1&-3\end{array}\right]$

Then B is the echelon form of A.

We use backward substitution to find the set of solutions.

1.

$-y=-3\\y=3$

2.

$3x+3y=6\\3x+3(3)=6\\x=-1$

The system has unique solution $(x,y)=(-1,3)$