Using the substitution p=1/x, q=1/y solve the simultaneous equations 1/x

Question

-5/4=7, 2/x+1/y=3

Answer 1

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.