Solve the system by substitution: 2x + y = 7 and y = x - 1.

• A. (7/3, 2/3)
• B. (4, 2)
• C. (8/3, 5/3)
• D. (3, 1)

Answer: (C)

Substitution is used here: replace y in the first equation with the expression from the second equation, since y equals x minus 1. So 2x + (x - 1) = 7. Combine like terms to get 3x - 1 = 7, then 3x = 8, giving x = 8/3. Now find y by plugging x back into y = x - 1: y = 8/3 - 1 = 5/3. The pair (8/3, 5/3) satisfies both equations (checking: 2x + y = 16/3 + 5/3 = 21/3 = 7, and y = x - 1 = 8/3 - 1 = 5/3). Other options don’t satisfy both equations when checked in, so they’re not valid solutions.