Question

how to solve using elimination method... x-2y+4z=6 3y+9z=0 -2x+6y-z=-10

Answer 1

I would write the system into a matrix,
\[\left[\begin{matrix} 1 & -2 & 4 & 6\\ 0 & 3 & 9 & 0 \\ -2 & 6 & -1 & -10\end{matrix}\right]\]
Then use linear combinations of files.

Answer 2

For example, if you multiply the first row by 2 and sum first row with third row to substitute the third row,
\[2F_1+F_3→F_3\]
Then,
\[\left[\begin{matrix} 1 & -2 & 4 & 6 \\ 0 & 3 & 9 & 0 \\ 0 & 2 & 7 & 2\end{matrix}\right]\]

Answer 3

And then you can do,
\[2F_2-3F_3\rightarrow F_3\]
\[\left[\begin{matrix} 1 & -2 & 4 & 6 \\ 0 & 3 & 9 & 0 \\ 0 & 0 & -3 & -6 \end{matrix}\right]\]

Answer 4

Now you only have to do backsubstitution in,
\[ x -2y + 4z = 6 \\ 3y +9z= 0\\ -3z= -6 \]

Answer 5

\[z=2,y=-6,x=-14\]

Answer 6

thank you so much for helping me to find the answer...

Answer 7

You're welcome.