Solving a System of Equations with Gaussian Elimination

[ImAnEngineer]

Homework Statement

Show that the following equations can be solved for any a:
ax1 + 2x2 + ax3 = 5a
x1 + 2x2 + (2-a)x3 = 5
3x1 + (a+2)x2 + 6x3 = 15

2. The attempt at a solution
I thought I would do gaussian elimination to get it into reduced form (in a coefficient matrix), and see where I can go from there. But I don't know how to do Gaussian elimination because the coefficient of a certrain x1 is a...

Can anybody give a hint?

 

[Mark44]

Just use Gaussian elimination. For starters, add row 1 to -a times row 2, and add -3 times row 1 to a times row 3. That will eliminate the first entries in the 2nd and 3rd rows. Continue until you get the system in row-echelon form.

Alternatively, you can divide row 1 by a, but in doing so, you are tacitly assuming that a != 0.