Answer:
p = 13, q = 9
Step-by-step explanation:
Given the 2 equations
[tex]\frac{q}{2}[/tex] - [tex]\frac{p}{3}[/tex] = [tex]\frac{1}{6}[/tex] ( multiply through by 6 to clear the fractions )
3q - 2p = 1 → (1)
[tex]\frac{p}{2}[/tex] - [tex]\frac{q}{6}[/tex] = 5 ( multiply through by 6 to clear the fractions )
3p - q = 30 , that is
- q + 3p = 30 → (2)
Multiplying (2) by 3 and adding to (1) eliminates the term in q
- 3q + 9p = 90 → (3)
Add (1) and (3) term by term to eliminate q
7p = 91 ( divide both sides by 7 )
p = 13
Substitute p = 13 into (2) for corresponding value of q
- q + 3(13) = 30
- q + 39 = 30 ( subtract 39 from both sides )
- q = - 9 ( multiply both sides by - 1 )
q = 9
Thus p = 13 and q = 9
