Answer
$x=6$
$y=2$
$z=3$
Work Step by Step
Let $x$ denote Refrigerator
Let $y$ denote Dishwashers
Let $z$ denote Stove
$\begin{cases}
8x+10y+14z=110\\
16x+12y+10z=150\\
10x+18y+6z=114
\end{cases}$
Multiplying Equation 1 by -2 and adding it to Equation 2, results in new Equation 1.
$\begin{cases}
-16x-20y-28z=-220\\
16x+12y+10z=150\\
-- -- -- -- -- -\\
-8y-18z=-70
\end{cases}$
Multiplying Equation 3 by -8/5 and adding it to Equation 2, results in new Equation 3.
$\begin{cases}
16x+12y+10z=150\\
-16x-28.8y-9.6z=-182.4\\
-- -- -- -- -- --\\
-16.8y+0.4z=-32.4
\end{cases}$
Multiplying the new Equation 3 by 45 and adding it to the new Equation 1.
$\begin{cases}
-8y-18z=-70\\
-756y+18z=-1458\\
-- -- -- -- --\\
-764y=-1528
\end{cases}$
Therefore, $y=2$, substituting back in, $z=3$ and $x=6$
