# How do you solve using gaussian elimination or gauss-jordan elimination, 4x-3y= -1, 3x+4y= -3?

Jan 17, 2016

$x = - 0.52$
$y = - 0.36$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} 4 x - 3 y = - 1$
$\textcolor{w h i t e}{\text{XXX}} 3 x + 4 y = - 3$

In augmented matrix form:
[ (4, -3, "|", -1), (3, 4, "|",-3) ]

Starting with row 1 as the "pivot row" (and column 1 as the "pivot column")
Reduce the pivot row (by dividing by the pivot entry value) so the pivot entry $= 1$
[ (4/4, -3/4, "|", -1/4), (3, 4, "|",-3) ]=[ (1, -0.75, "|", -0.25), (3, 4, "|",-3) ]

Reduce the non-pivot rows so their pivot column entries are $0$
(by subtracting the pivot row times the non-pivot row, pivot column entry from the non-pivot row)
[ (1, -0.75, "|", -0.25), (3-3xx1, 4-3xx(-0.75), "|",-3-3xx(-0.25)) ]=[ (1, -0.75, "|", -0.25), (0, 6.25, "|",-2.25) ]

Advance the pivot row (so it is now row 2)
and repeat the above process:
[ (1, -0.75, "|", -0.25), (0, 1, "|",-0.36) ]

then
[ (1, 0, "|", -0.52), (0, 1, "|",-0.36) ]