Answer
Inconsistent
Work Step by Step
We are given the system of equations:
$\begin{cases}
x-4y+3z=15\\
-3x+y-5z=-5\\
-7x-5y-9z=10
\end{cases}$
Use the elimination method. Multiply the first equation by 3 and add it to the second to eliminate $x$. Then multiply the first equation by 7 and add it to the third to eliminate $x$:
$\begin{cases}
-3x+y-5z+3(x-4y+3z)=-5+3(15)\\
-7x-5y-9z+7(x-4y+3z)=10+7(15)
\end{cases}$
$\begin{cases}
-3x+y-5z+3x-12y+9z=-5+45\\
-7x-5y-9z+7x-28y+21z=10+105
\end{cases}$
$\begin{cases}
-11y+4z=40\\
-33y+12z=115
\end{cases}$
Multiply the first equation by -3 and add it to the second to eliminate $y$ and find $z$:
$-3(-11y+4z)-33y+12z=-3(40)+115$
$33y-12z-33y+12z=-120+115$
$0=-5$
We got a false statement; therefore the system is inconsistent.
