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:

152x − 378y = −74  …… (1)

−378x + 158y = −604  …… (2)

Step 1: Multiply the Equations to Eliminate One Variable

Multiply equation (1) by 158 and equation (2) by 378:

(1) × 158 ⇒ 24016x − 59724y = −11692  …… (3)

(2) × 378 ⇒ −142884x + 59724y = −228312  …… (4)

Step 2: Add Equations (3) and (4)

24016x − 59724y − 142884x + 59724y = −11692 − 228312

−118868x = −240004

⇒ x = ^−240004/_−118868

⇒ x = 2

Step 3: Substitute x = 2 in Equation (1)

152(2) − 378y = −74

304 − 378y = −74

−378y = −378

⇒ y = 1

Final Answer

∴ The solution of the given system of equations is:

x = 2 and y = 1

Conclusion

Thus, by using the elimination method, we find that the solution of the given system of linear equations is (2, 1).