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 + 5y = 7  …… (1)

3/x + 4y = 5  …… (2)

Step 1: Substitute 1/x = z

Let 1/x = z

Then equations (1) and (2) become:

4z + 5y = 7  …… (3)

3z + 4y = 5  …… (4)

Step 2: Express One Variable in Terms of the Other

From equation (3):

5y = 7 − 4z

⇒ y = ^{7 − 4z}/₅  …… (5)

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

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

3z + 4( ^{7 − 4z}/₅ ) = 5

Multiply the whole equation by 5:

15z + 28 − 16z = 25

−z = −3

⇒ z = 3

Step 4: Find the Value of x

Since z = 1/x,

1/x = 3

⇒ x = ¹/₃

Step 5: Find the Value of y

Substitute z = 3 in equation (5):

y = ^{7 − 4(3)}/₅

y = ^{7 − 12}/₅

y = −1

Final Answer

∴ The solution of the given system of equations is:

x = ¹/₃ and y = −1

Conclusion

Thus, by substituting 1/x = z and using the substitution method, we find that the solution of the given system of equations is (1/3, −1).