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if p*x+q*y=p-q and q*x+p*y=p+q find the values of x and y

if p*x+q*y=p-q and q*x+p*y=p+q find the values of x and y
 

Grade:9

1 Answers

Ramvardhan
25 Points
8 years ago
px + qy = p – q -----> Equation 1
qx + py = p + q -----> Equation 2
 
Add both the equations.
px + qy + qx + py = p – q + p + q
=> p(x+y) + q(x+y) = 2p
=> (p+q)(x+y) = 2p
=> x+y = 2p/p+q -----> Equation 3
 
Now subtract equation 1 from 2.
After simplification similarly like before, you will get :
x-y = 2q/q-p -----> Equation 4
 
Now add equation 3 and 4 and simplify to get the value of x. Then subract equation 4 from 3 and simplify to get the value of y.
 
Finally x =(q2 + 2pq – p2) / (q2 – p2) 
           y = (p2 + q2) / (p2 - q2)
 

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