(5)/(x-1)+(1)/(y-2)=(7)/(4) (6)/(x-1)-(2)/(y-2)=(1)/(2)

3 min read Jun 16, 2024

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)/(x-1) + (1)/(y-2) = (7)/(4)

(2) (6)/(x-1) - (2)/(y-2) = (1)/(2)

Step 1: Assign Variables

To simplify the equations, let's assign new variables:

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):

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:

Solution

The solution to the system of equations is: