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.

$3x+y+z=14$

$-x+2y-3z=-9$

$5x-y+5z=30$

-
The problem is that the number of variable that you have to deal is too much. Try to think how to reduce it. If you add 3 times of second line to first line, and add 5 times of second line to third line, then the x term will be erased in other two equation. Now we get one equation with 3 variable and two equations with 2 variable (one variable, $x$, was killed so far). Now do it yourself. – fiverules Dec 16 '13 at 2:34

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.

-

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:

$$\left[ \begin{array}{ccc|c} 3 & 1 & 1 & 14\\ -1 & -2 & -3 & -9\\ 5 & -1 & 5 & 30 \end{array} \right]$$

-