Question 1090279
<br>The matrix for the given equations is<br>
{{{matrix(3,4,1,0,-1,-3,0,1,1,9,1,0,1,7)}}}<br>
We first want to get "1 0 0" in column 1.  It is already nearly the way we want it; we just need to get a 0 in row 3.  To do that, we can replace row 3 with (row 3 - row 1).
R3 <-- R3-R1: 1-1=0; 0-0=0; 1-(-1)=2; 7-(-3)=10:<br>
{{{matrix(3,4,1,0,-1,-3,0,1,1,9,0,0,2,10)}}}<br>
Next we can make smaller numbers in the matrix by dividing row 3 by 2:<br>
{{{matrix(3,4,1,0,-1,-3,0,1,1,9,0,0,1,5)}}}<br>
After this, the second column is already the way we want it.  So now we use row 3 to get "0 0 1" in column 3.
R1 <-- R1+R3: 1+0=1; 0+0=0; 1+(-1)=0; -3+5=2
R2 <-- R2-R3: 0-0=0; 1-0=1; 1-1=0; 9-5=4<br>
{{{matrix(3,4,1,0,0,2,0,1,0,4,0,0,1,5)}}}<br><br>
The solution to the system of equations is x=2, y=4, z=5.