Question

Use gauss-jordan elimination to solve the following system of equations. 3x 5y = 7 6x − y = −8

Answer 1

Yasss

3x+5y=7
6x-1y=-8
so what you do is remove the placeholders ad put them in matrix form

so
$\left[\begin{array}{ccc}3&5|&7\\6&-1|&-8\end{array}\right]$
eliminate one placeholder at a time

remember: first column=x, 2nd column=y, 3rd column=constant


let's eliminate x's
times first row by -2
$\left[\begin{array}{ccc}-6&-10|&-14\\6&-1|&-8\end{array}\right]$
add that to 2nd row
$\left[\begin{array}{ccc}-6&-10|&-14\\0&-11|&-22\end{array}\right]$
divide last row by -11
$\left[\begin{array}{ccc}-6&-10|&-14\\0&1|&2\end{array}\right]$


eliminate y's now
multiply last row by 10
$\left[\begin{array}{ccc}-6&-10|&-14\\0&10|&20\end{array}\right]$
add 2nd row to first row
$\left[\begin{array}{ccc}-6&0|&6\\0&10|&20\end{array}\right]$
divide first row by -6
$\left[\begin{array}{ccc}1&0|&-1\\0&10|&20\end{array}\right]$
divide last row by 10
$\left[\begin{array}{ccc}1&0|&-1\\0&1|&2\end{array}\right]$
$\left[\begin{array}{ccc}x&y|&c\\x&y|&c\end{array}\right]$
1x=-1
1y=2

x=-1
y=2
(-1,2)