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:

23x − 29y = 98  …… (1)

29x − 23y = 110  …… (2)

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

(29x − 23y) − (23x − 29y) = 110 − 98

6x + 6y = 12

⇒ x + y = 2  …… (3)

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

(23x − 29y) + (29x − 23y) = 98 + 110

52x − 52y = 208

⇒ x − y = 4  …… (4)

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

Add equations (3) and (4):

(x + y) + (x − y) = 2 + 4

2x = 6

⇒ x = 3

Substitute x = 3 in equation (3):

3 + y = 2

⇒ y = −1

Final Answer

∴ The solution of the given system of equations is:

x = 3 and y = −1

Conclusion

Thus, by using the elimination method, we find that the solution of the given system of linear equations is (3, −1).