Answer:
p + q = 13/4
Step-by-step explanation:
p² - q² = 7
p - q = 2
Use substitution.
p = 2 + q
(2 + q)² - q² = 7
Expand (2 + q)² with FOIL - first, outer, inner, last
(2 + q)(2 + q)
4 + 2q + 2q + q²
4 + 4q + q²
Subtract q².
4 + 4q + q² - q² = 7
4 + 4q = 7
Combine like-terms.
4q = 3
Divide by 4 to isolate q.
q = 3/4
Plug q into the equation to find p.
p - q = 2
p - (3/4) = 2
Add 3/4 to both sides.
p = 11/4
Add p and q.
11/4 + 3/4
= 13/4
