Universal pet house sells vinyl doghouses and treated lumber doghouses. It takes the company 5 hours to build a vinyl doghouse and 2 hours to build a treated lumber doghouse. The company dedicates 50 hours every week towards building doghouses. It takes an additional hour to paint each vinyl doghouses and an additional 2 hours to assemble each treated lumber doghouse. The company dedicates 30 hours every week towards assembling and painting doghouse.
Write a system of equation that represent the production time needed to build each doghouse and the production time needed for painting and assembling each dog house. Use X to represent the number of vinyl doghouses and Y to represent the number of treated lumber doghouses