Question

9x-y+z = -34x+ 2y-3z = 4x-3y + 2z = -11

Answer 1

We have the system of linear equations:

$\begin{gathered} 9x-y+z=-3 \\ 4x+2y-3z=4 \\ x-3y+2z=-11​ \end{gathered}$

We can start substituting variables as:

$y=9x+z+3$$\begin{gathered} 4x+2(9x+z+3)-3z=4 \\ 4x+18x+2z+6-3z=4 \\ 22x-z+6=4 \\ z=22x+6-4 \\ z=22x+2 \end{gathered}$$\begin{gathered} x-3y+2z=-11 \\ x-3(9x+z+3)+2(22x+2)=-11 \\ x-3\lbrack9x+(22x+2)+3\rbrack+2(22x+2)=-11 \\ x-27x-66x-6-9+44x+4=-11 \\ (1-27-66+44)x+(-6-9+4+11)=0 \\ -48x+0=0 \\ x=\frac{0}{-48}=0 \end{gathered}$$z=22x+3=22\cdot0+3=3$$y=9x+z+3=9\cdot0+3+3=6$

Then, the solution to this system of equations is:

$x=0,y=6,z=3$