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:

x − y + z = 4  …… (1)

x + y + z = 2  …… (2)

2x + y − 3z = 0  …… (3)

Step 1: Eliminate y from Equations (1) and (2)

Add equations (1) and (2):

(x − y + z) + (x + y + z) = 4 + 2

2x + 2z = 6

⇒ x + z = 3  …… (4)

Step 2: Eliminate y from Equations (2) and (3)

Subtract equation (2) from equation (3):

(2x + y − 3z) − (x + y + z) = 0 − 2

x − 4z = −2  …… (5)

Step 3: Solve Equations (4) and (5)

From equation (4):

x = 3 − z  …… (6)

Substitute x from equation (6) into equation (5):

(3 − z) − 4z = −2

3 − 5z = −2

⇒ 5z = 5

⇒ z = 1

Step 4: Find the Value of x

Substitute z = 1 in equation (6):

x = 3 − 1

⇒ x = 2

Step 5: Find the Value of y

Substitute x = 2 and z = 1 in equation (2):

2 + y + 1 = 2

⇒ y = −1

Final Answer

∴ The solution of the given system of equations is:

x = 2, y = −1 and z = 1

Conclusion

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