Answer
$x=1$
$y=2$
$z=2$.
Work Step by Step
Let $x$ denote Toast
Let $y$ denote Cottage cheese
Let $z$ denote Fruit
Thus,
$\begin{cases}
100x+120y+60z=460\\
x+5y=11\\
2x+2z=6
\end{cases}$
Multiplying Equation 2 by -2 and adding it to Equation 3, results in new Equation 3.
$\begin{cases}
-2x-10y=-22\\
2x+2z=6\\
-- -- --\\
-10y+2z=-16
\end{cases}$
Dividing both sides by 2, $-5y+z=-8$.
Multiplying Equation 2 by -100 and adding it to Equation 1, results in new Equation 1.
$\begin{cases}
-100x-500y=-1100\\
100x+120y+60z=460\\
-- -- -- -- --\\
-380y+60z=-640
\end{cases}$
Dividing both sides by 20, $-19y+3z=-32$.
Multiplying new Equation 3 by -3 and adding it to new equation 1.
$\begin{cases}
15y-3z=24\\
-19y+3z=-32\\
-- -- -- --\\
-4y=-8
\end{cases}$
Thus, $y=2$, Substituting back in, $z=2$ and $x=1$
