Solving a System of Equations with Two Unknowns
This article will guide you through the process of solving a system of equations with two unknowns, using the example of the following equations:
(1) (5)/(x1) + (1)/(y2) = (7)/(4)
(2) (6)/(x1)  (2)/(y2) = (1)/(2)
Step 1: Assign Variables
To simplify the equations, let's assign new variables:
 Let u = (1)/(x1)
 Let v = (1)/(y2)
Substituting these new variables into our original equations, we get:
(1) 5u + v = 7/4 (2) 6u  2v = 1/2
Step 2: Solve for One Variable
Now we have a simpler system of equations that we can solve using various methods. Let's use the elimination method.

Multiply Equation (1) by 2: This will allow us to eliminate 'v' when we add the equations together.
 10u + 2v = 7/2

Add the modified Equation (1) to Equation (2):
 16u = 8/4 = 2
 u = 1/8
Step 3: Solve for the Second Variable
Now that we know the value of 'u', substitute it back into either Equation (1) or (2) to solve for 'v'. Let's use Equation (1):
 5(1/8) + v = 7/4
 5/8 + v = 7/4
 v = 7/4  5/8
 v = 9/8
Step 4: Substitute Back to Find Original Variables
We've found the values for 'u' and 'v', but remember, we need to find 'x' and 'y'. Substitute the values back into our original variable assignments:

u = (1)/(x1) = 1/8
 This gives us x1 = 8, therefore x = 9

v = (1)/(y2) = 9/8
 This gives us y2 = 8/9, therefore y = 26/9
Solution
The solution to the system of equations is:
 x = 9
 y = 26/9