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:

21x + 47y = 110  …… (1)

47x + 21y = 162  …… (2)

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

(47x + 21y) − (21x + 47y) = 162 − 110

26x − 26y = 52

⇒ x − y = 2  …… (3)

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

(21x + 47y) + (47x + 21y) = 110 + 162

68x + 68y = 272

⇒ 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 (4):

3 + y = 4

⇒ 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).