minimizing subjective to. Math help please

Question

Minimize

Subject to

What is the minimum and the x and y points

Answer 1

18-2y=10-y

y = 8, x=1 (1,8) is one vertex

(9,0) and (0,9) two more vertices, (3,6) is another

(0,0) another

plug them into the objective function and see which is smallest

2x+5y

2+40=42

18, 45

36

(9,0) makes z =18

but (0,0) makes z=0