Using the substitution p=1/x, q=1/y solve the simultaneous equations 1/x
-5/4=7, 2/x+1/y=3
Starting with the first equation: 1/x - 5/4 = 7
Multiply both sides by 4x to eliminate the denominators:
4 - 5x = 28x
Adding 5x to both sides and subtracting 4 from both sides:
33x = 4
Dividing both sides by 33:
x = 4/33
Now, let's move to the second equation:
2/x + 1/y = 3
Substitute p = 1/x and q = 1/y:
2p + q = 3
Now, we have a system of equations:
p = 4/33
2p + q = 3
Substituting p into the second equation:
2(4/33) + q = 3
Multiplying 2 by 4/33:
8/33 + q = 3
Subtracting 8/33 from both sides:
q = 3 - 8/33
Simplifying the right side:
q = (99 - 8)/33
q = 91/33
Therefore, the solution is p = 4/33 and q = 91/33.