Determine Number of Coins A jar holding 1 cent, 5 cent and 10 cent coins contains twelve coins with a total value of 86 cent. How many coins of each type are in the box? (Preferably using an augmented matrix) My attempt so far is (let x= no. of 1 cent coins, y = etc...): $$ x+y+z=12\\\ x+5y+10z=86\\\ x\geq0, y\geq0, z\geq0 $$ but I'm not sure how to formulate the last condition correctly in an augmented matrix.

Hint: Subtract the first from the second to get: $$4y+9z=74 \Rightarrow z=\frac{74-4y}{9}=\frac{2(37-2y)}{9}.$$