Question 53783
P+R=4
PQ+R=10
P+QR=14

To solve, add the second and third equations together:
  PQ+R=10
 + P+QR=14
equals: PQ+R+P+QR=24
factoring: (R+P)+Q(P+R)=24
substituting 4 for P+R:
      (4) + Q(4)=24
subtracting 4 from both sides:
4+4Q-4=24-4
4Q=20,  dividing by 4:
Q=5.
Using R=4-P and PQ+R=10, we get:
5P+4-P=10
4P+4=10  subtracting 4,
4P=6  dividing by 4,
P=6/4 or 3/2=1.5
Using P=4-R and P+QR=14:
4-R+5R=14
4+4R=14  subtracting 4,
4R=10  dividing by 4,
R=10/4 or 5/2=2.5

so, Q=5, P=1.5, R=2.5
1.5+2.5=4  ok
5*1.5+2.5=7.5+2.5=10  ok
1.5+5*2.5=1.5+12.5=14  ok