Solve the System of Linear Equations Using Substitution Method

Video Explanation

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

Solution

Question: Solve the following system of equations:

4/x + 3y = 8  …… (1)

6/x − 4y = −5  …… (2)

Step 1: Substitute 1/x = z

Let 1/x = z

Then equations (1) and (2) become:

4z + 3y = 8  …… (3)

6z − 4y = −5  …… (4)

Step 2: Express One Variable in Terms of the Other

From equation (3):

3y = 8 − 4z

⇒ y = ^{8 − 4z}/₃  …… (5)

Step 3: Substitute the Value of y in Equation (4)

Substitute y from equation (5) into equation (4):

6z − 4( ^{8 − 4z}/₃ ) = −5

Multiply the whole equation by 3:

18z − 32 + 16z = −15

34z = 17

⇒ z = ¹/₂

Step 4: Find the Value of x

Since z = 1/x,

1/x = 1/2

⇒ x = 2

Step 5: Find the Value of y

Substitute z = 1/2 in equation (5):

y = ^{8 − 4(1/2)}/₃

y = ^{8 − 2}/₃

y = ⁶/₃

y = 2

Final Answer

∴ The solution of the given system of equations is:

x = 2 and y = 2

Conclusion

Thus, by substituting 1/x = z and using the substitution method, we find that the solution of the given system of equations is (2, 2).