SOLUTION: Find the value of Q P+R=4 Q*P+R=10 P+Q*R=14 Q=???

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Question 53651: Find the value of Q
P+R=4
Q*P+R=10
P+Q*R=14
Q=???
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Find the value of Q

       P + R =  4
      QP + R = 10
      P + QR = 14

This is a system of 3 equations in 3 unknowns.

Solve the first equation for P

           P = 4 - R

Substitute (4 - R) for P in the 2nd equation:
      QP + R = 10
Q(4 - R) + R = 10
 4Q - QR + R = 10

Substitute (4 - R) for P in the 3rd equation:
      P + QR = 14
(4 - R) + QR = 14
  4 - R + QR = 14
     -R + QR = 10

Now we have this system of two equations in 2 unknowns

 4Q - QR + R = 10
     -R + QR = 10

Now we write the terms on the left of the second equation
in the opposite order, draw a line and add vertically
term by term: 

 4Q - QR + R = 10
      QR - R = 10
 ----------------
 4Q          = 20
           Q = 5

Substitute 5 for Q in the equation QR - R = 10:

      QR - R = 10
      5R - R = 10
          4R = 10
           R = 10/4
           R = 5/2 

Substitute 5/2 for R in the equation P = 4 - R:

           P = 4 - R
           P = 4 - 5/2
           P = 8/2 - 5/2
           P = 3/2

So (P, Q, R) = (3/2, 5, 5/2)

Edwin