Answer
l=5
Pivots: 2,-6
Work Step by Step
Multiply by l = $\frac{10}{2}$ = 5, and subtract to find 2x + 3y = 1 and -6y = 6. Pivots 2, -6.
Our goal should be to form a triangular system of equations, such that in equation 1 all of our coefficients are non-zero, and in equation two our first coefficient is zero and second coefficient is non-zero.
Start with your given system of equations:
2x+3y=1
10x+9y=11
Rewrite the equations as an augmented matrix:
{2 3 | 1}
{10 9 | 11}
Multiply the first row vector of the matrix by 5 (the value of l), and subtract the first row vector from the second row vector to create a new value for the second row vector of your matrix. ($R_{2}$-$R_{1}$-->$R_{2}$)
{10 9 | 11} - {10 15 | 5} = {0 -6 | 6}
Our new matrix is now:
{2 3 | 1}
{0 -6 | 6}
Which means our system of linear equations is:
2x+3y=1
(0x)-6y=6
This system of linear equations is now triangular and has pivot points. As a reminder, a pivot point is the first non-zero entry in a row when dealing with elimination. This would make our pivot coefficients 2 and -6.
