13. A house-painting company charges $360 plus $9 per hour. Another
company charges $270 plus $18 per
hour. Write an equation and solve to
find
a) How long is a job for which both
companies will charge the same
amount?
b) What will that cost be?

So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.

Subtract 2 from all the first numbers and add 3 to all the second ones for new coordinates