Solve Systems Using Matrix Row Operations

$$\text{Spoil Your Dog Day}$$

===

Today (August 10) is National Spoil Your Dog Day!

You decide to spoil your dog by giving him toys, $x$, treats, $y$, and walks, $z$.

A toy costs $\$$10, a treat costs $\$$1, and a walk, in theory, costs $\$$2 since your time is worth something. You only have $\$$76 to spend.

Your dog gets 300 happiness from a toy, 600 happiness from a treat, and 900 happiness from a walk. Your dog gets overwhelmed and exhausted after 10,200 happiness.

Buying a toy takes up 10 minutes of your day, buying a treat takes up 6 minutes, and a walk takes up 30 minutes. You decide to spent 3.8 hours on your dog today.