Final answer:
The solution is p=2 and q=-1.
Step-by-step explanation:
To solve the simultaneous equations 2/x+1/y=3 and 1/x-5/y=7, we can use substitution method.
We have p=1/x and q=1/y, so the equations can be rewritten as:
2p + q = 3 (equation 1)
p - 5q = 7 (equation 2)
From equation 1, we can isolate q:
q = 3 - 2p
Substituting this value of q into equation 2:
p - 5(3 - 2p) = 7
Simplifying the equation:
p - 15 + 10p = 7
Combining like terms:
11p - 15 = 7
Adding 15 to both sides:
11p = 22
Dividing both sides by 11:
p = 2
Substituting the value of p back into equation 1:
2(2) + q = 3
4 + q = 3
Subtracting 4 from both sides:
q = -1
Therefore, the solution to the simultaneous equations is p=2 and q=-1.