Question 1196103
<pre>
{{{system(3x-2y+5z=8,
2x-3y+4z=15)}}}

{{{(matrix(2,5,
3,-2,5,"|",8,
2,-3,4,"|",15))}}}

To make the 2 on row 2 column 1 become 0,
 
-2R1+3R2->R2

{{{(matrix(2,5,
3,-2, 5,"|",8,
0,-5,2,"|",29))}}}

To make the -2 on row 1 column 2 become 0,

-2R2+5R1->R1

{{{(matrix(2,5,
15, 0, 21,"|",-18,
 0,-5,  2,"|" ,29))}}}
To make the leading coefficients become 1,

(1/15)R1->R1
(-1/5)R2->R2

{{{(matrix(2,5,
 1, 0, 7/5,"|",-6/5,
 0, 1,-2/5,"|", -29/5))}}}

{{{system(1x+0y+expr(7/5)z=-6/5, 0x+1y-expr(2/5)z=-29/5)}}}

{{{system(x+expr(7/5)z=-6/5, y-expr(2/5)z=-29/5)}}}

{{{system(x=-6/5-expr(7/5)z, y=-29/5+expr(2/5)z)}}}

{{{(matrix(1,5,   x,",",y,",",z))}}}{{{""=""}}}{{{(matrix(1,5,   -6/5-expr(7/5)z,",",-29/5+expr(2/5)z,",",z))}}}

Edwin</pre>