i need help setting up a system of two equations

Question

Define your variables and set up a system of two equations and two unknowns for the following problem, then solve the system and answer the question. Show all your work!

 

Excedrin surveyed wrokers in various professions who get headaches at least once a year on the job. Nine more accountants than waiters/waitresses in the survey got a headach. If the combined number of accountant and waiters/waitresses that got a headache was 163, how many people in each of those professions got a headache? What method did you use to solve this problem?

Answer 1

Number of accountants who got headaches -- x

Number of waiters/waitresses who got headaches -- y

 

x = y + 9    (nine more accountants got headaches)

x + y = 163    (the combined number is 163)

 

Plug the right side of the top equation into "x" in the bottom equation:

 

y + 9 + y = 163

 

Collect like terms:

 

2y + 9 = 163

 

Solve for y:

 

2y = 154

 

y = 77

 

Plug this value of y back into the first equation and solve for x:

 

x = 77 + 9

 

x = 86

 

This is the substitution method.