Solve the System of Linear Equations Using Elimination Method

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question: Solve the following system of equations:

99x + 101y = 499  …… (1)

101x + 99y = 501  …… (2)

Step 1: Subtract Equation (1) from Equation (2)

(101x + 99y) − (99x + 101y) = 501 − 499

2x − 2y = 2

⇒ x − y = 1  …… (3)

Step 2: Add Equation (1) and Equation (2)

(99x + 101y) + (101x + 99y) = 499 + 501

200x + 200y = 1000

⇒ x + y = 5  …… (4)

Step 3: Solve Equations (3) and (4)

Add equations (3) and (4):

(x − y) + (x + y) = 1 + 5

2x = 6

⇒ x = 3

Substitute x = 3 in equation (4):

3 + y = 5

⇒ y = 2

Final Answer

∴ The solution of the given system of equations is:

x = 3 and y = 2

Conclusion

Thus, by using the elimination method, we find that the solution of the given system of linear equations is (3, 2).