Question

Please please help! I keep getting horribly wrong asnwers!


x - 3y + 4z = -9
2x + y + 3z = 6
x - 4y + 3z = -9

Answer 1

A) x - 3y + 4z = -9
B) 2x + y + 3z = 6
C) x - 4y + 3z = -9
A+B+C = ?
say...

Answer 2

\[\begin{cases}x-3y+4z=-9\\2x+y+3z=6\\x-4y+3z=-9\end{cases}\]
Solving for \(x\) in the third equation:
\[x=4y-3z-9\]
Substituting this into both the first and second equation (thus eliminating \(x\):
\[\begin{cases}(4y-3z-9)-3y+4z=-9\\2(4y-3z-9)+y+3z=6\end{cases}~~\Rightarrow~~\begin{cases}y+z=0\\9y-3z=24\end{cases}\]
Solving for \(y\) in the first equation yields \(y=-z\). Plug this into the second equation:
\[9(-z)-3z=24~~\Rightarrow~~-12z=24~~\Rightarrow~~z=-2\]
\[z=-2~\Rightarrow~y=2~\Rightarrow~x=5\]