Question 637356
Given
(1) P + R = 4
(2) QP + R = 10
(3) QR + P = 14
Recognize that you need the products QP and QR, so simply multiple both sides of (1) by Q and obtain
(4) QP + QR = 4Q
Now add (2) and (3) to obtain
(5) QP + QR + R + P = 10 + 14
Substitute (4) into (5) to get
(6) 4Q + R + P = 24
Substitute (1) into (6) to get
(7) 4Q + 4 = 24
    4Q = 20
     Q = 5
Now substitute Q into (2)
(2)' 5P + R = 10
Use (2)' and (1) to solve simultaneously to get P nad R
  5P + R = 10
   P + R = 4
  5(4 - R) + R = 10
  20 - 5R + R = 10
  4R = 10
   R = 5/2
Use (1) and R to get
   P + 5/2 = 4 
   P = 3/2
Now check your answers in (2) and (3)
Is (5*(3/2) + 5/2 = 10)?
Is (15/2 + 5/2 = 10)?
Is (20/2 = 10)?
Is (10 = 10)? Yes

Is (5*(5/2) + 3/2 = 14)?
Is (25/2 + 3/2 = 14)?
Is (28/2 = 14)?
Is (14 = 14)? Yes

Your answer is P = 3/2, Q = 5 and R = 5/2