To eliminate p, multiply the first equation by two, the second by 5 and add the results.
-5p+q/2=-3/2......(1)
2p+3q/2=4......(2)
(1)x2
(-5p)x2+(q/2)x2=(-3/2)x2
-10p+q=-3
(2)x5
(2p)x5+(3q/2)x5=(4)x5
10p+15q/2=20
(-10p+q)+(10p+15q/2)=-3+20
16q/2=17
↓↓↓ ??