simutaneuos equation by elimination method

Question

3(p+2) = 4(q-3)

(3q+4)/2  - (p-5)/6 =0

Answer 1

3p+6=4q-12,

3p-4q=-18 ①

(3q+4)/2-(p-5)/6=0, multiply through by 6:

9q+12-p+5=0,

-p+9q=-17, multiply through by 3:

-3p+27q=-51 ②

Add ① and ②:

3p-4q=-18

-3p+27q=-51

23q=-69, q=-3.

Substitute in ① for q:

3p+12=-18,

3p=-30, p=-10.

CHECK

3(p+2)=3(-8)=-24; 4(q-3)=4(-6)=-24✔️

(3q+4)/2-(p-5)/6=(-9+4)/2+15/6=-5/2+5/2=0✔️

ANSWER: p=-10, q=-3.