solve the simultaneous equation
1/y + 1/x =5 .......(i )
1/x - 1/y =1 ........(i i )
Just add them, the 1/y's will drop out
2/x = 6
6x = 2
x = 1/3
sub into the original first
1/y + 1/(1/3) = 5
1/y + 3 = 5
1/y = 2
y = 1/2
Add the two equations to give you:
2/x = 6
Solve for x, then y.
thanks to all, God bless you
To solve the given simultaneous equations:
Equation (i): 1/y + 1/x = 5
Equation (ii): 1/x - 1/y = 1
Let's rearrange equation (ii) to get the value of 1/y in terms of 1/x:
1/y = 1 + 1/x
Now, substitute this value of 1/y into equation (i):
1/(1 + 1/x) + 1/x = 5
To solve this equation algebraically, we can follow these steps:
Step 1: Find the common denominator of the fractions.
Multiply the whole equation by x(1 + 1/x) to eliminate the denominators:
x + (1 + 1/x) = 5x(1 + 1/x)
x + 1 + 1/x = 5(x + 1)
x + 1 + 1/x = 5x + 5
Step 2: Simplify the equation.
Combine like terms on both sides of the equation:
(x + 1/x) + 1 = 5x + 5
Step 3: Move all terms to one side of the equation:
(x + 1/x) - 5x = 5 - 1
Step 4: Combine like terms and simplify further:
(x^2 + 1) - 5x^2 = 4x - 4
Step 5: Rearrange terms to get a quadratic equation:
-x^2 + 4x + 1 = 0
This quadratic equation can be solved using the quadratic formula or factoring. Once you find the values of x, substitute them back into equations (i) or (ii) to solve for y.