on solving p/X + q/y = m , q/X + p/y = n we get ?
Answers
Answer:
x/y = (mp-nq)/(mq-np)
Step-by-step explanation:
Clearly from the given questions both x, y aren't zeroes. i. e., (x!= 0 && y! =0)
Adding both equations..
We get (p+q)(1/x +1/y) =(m +n )
1/x + 1/y =(m+n)/(p +q)
Multiply with p on both sides and subtract from p/x +q/y =m
then we get the value of y as (mq-np) /(p+q)
Solving in a similar fashion for x or by symmetry we get x=(mp-nq) /(p+q)
Hence the required value,
x/y = (mp-nq)/(mq-np)
Answer:
x = pm - qn/p² - q², y = pn - qm/p² - q²
Step-by-step explanation:
p/x + q/y = m -------- [1]
q/x + p/y = n. --------- [2]
multiply[1] by q and [2] by p
and subtract [1] from [2]
pq/x + p²/y = pn --------- ([2] multiplied by p)
pq/x + q²/y = qm --------- ( [1] multiplied by q)
- - -
-------------------------------
p² - q²/y = pn - qm
=> y = pn - qm/p² - q²
Now to find x,
multiply[1] by p and [2] by q
and subtract [2] from [1]
p²/x + pq/y = pm --------- ([1] multiplied by p)
q²/x + pq/y = qn --------- ( [2] multiplied by q)
- - -
-------------------------------
p² - q²/x = pm - qn
=> x = pm - qn/p² - q²