Solve the simultaneous equation 3/p -2/q=7/12, p/3+q/4=1

Answer 1

p=9, q=-8 or p=q=about 7/4

plug them in

9/3 + -8/4 = 1

3/9 -2/-8 = 1/3 +1/4 = 7/12

(p,q) = (9,-8) works

(7/4)/3 + (7/4)4 = 7/12 +7/16 = (28 +21)/48 = 49/48 = about 1

3/(7/4) - 2/(7/4) = 12/7 - 8/7 = 4/7 =48/84 = about 49/84 = about 7/12

it works (p,q) = about (1.75, 1.75)

those two solutions found by graphing the two equations and finding their two intersection points

or try substitution elimination

but it's so tedious, likely mistakes very error prone

p/3 +q/4 =1 multiply by 12

4p +3q =12

p = (12-3q)/4 = 3 -3q/4

3/p -2/q= 7/12 multiply by 12pq

36q -24p = 84pq

36q - 24(3-3q/4) = 84q(3-3q/4)

54q - 72 = 252q -63q^2

63q^2 - 198q - 72 = 0

q= about 3.47 or - 1/3

p = 3-.75q = about .4 or 3.25

(p,q) = about (2/5, 3.47) or (3.25, 1/3) nope. they don't work. mistake(s) somewhere.