3p+4q-5r=-2 | 4p-2q-3r=12 | p+5q+2r=3. ditanya p,q dan r ?

diketahui:
3p+4q-5r = -2 (persamaan 1)
4p-2q-3r = 12 (persamaan 2)
p+5q+2r = 3 (persamaan 3)

ditanya:
p, q, r =?

jawab:
eliminasi persamaan 1 dan 3
3p+4q-5r = -2 | ×1
p+5q+2r = 3 | ×3
---------------------------
3p+4q-5r = -2
3p+15q+6r = 9
----------------------- -
-11q-11r = -11
-q-r = -11
q+r = 11 (persamaan 4)

eliminasi persamaan 2 dan 3
4p-2q-3r = 12 | ×1
p+5q+2r = 3 | ×4
----------------------------
4p-2q-3r = 12
4p+20q+8r = 12
------------------------- -
-22q-11r = 0
-2q-r = 0
-2q = r

nilai r disubstitusi ke perasamaan 4
q+r = 11
q + (-2q) = 11
-q = 11
q = -11

nilai q disubstitusi ke persamaan 4
q+r = 11
-11 + r = 11
r = 11 + 11
= 22

substitusi persamaan 3
p+5q+2r = 3
p + 5×(-11) + 2 × 22 = 3
p - 55 + 44 = 3
p - 11 = 3
p = 3+11
= 14

jadi nilai p = 14, q = -11, dan r = 22