Thanks in advance if you are reading this...
I have a math midterm in several days and i have found an equation i cannot solve. If possible can you please show your steps. I have the misfortune of a teacher who looks for these to assign( i get every other problem assigned except this particular one)
Solve system of equations.
$3x+y+z=14$
$-x+2y-3z=-9$
$5x-y+5z=30$
On
This is a standard method for solving linear equations: http://en.wikipedia.org/wiki/Gaussian_elimination
Transform system to its matricial form and then eliminate:
Here is your system in matricial form:
$$ \left[ \begin{array}{ccc|c} 3 & 1 & 1 & 14\\ -1 & -2 & -3 & -9\\ 5 & -1 & 5 & 30 \end{array} \right] $$
Add $3*$ equation 2 to equation 1. The result is a linear equation in $y$ and $z$. Now add $5*$ equation 2 to equation 3. You get a second linear equation in $y$ and $z$. Solve these and back-substitute.