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 = 14  …… (1)

3/x − 4y = 23  …… (2)

Step 1: Substitute 1/x = z

Let 1/x = z

Then equations (1) and (2) become:

4z + 3y = 14  …… (3)

3z − 4y = 23  …… (4)

Step 2: Express One Variable in Terms of the Other

From equation (3):

3y = 14 − 4z

⇒ y = ^{14 − 4z}/₃  …… (5)

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

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

3z − 4( ^{14 − 4z}/₃ ) = 23

Multiply the whole equation by 3:

9z − 56 + 16z = 69

25z = 125

⇒ z = 5

Step 4: Find the Value of x

Since z = 1/x,

1/x = 5

⇒ x = ¹/₅

Step 5: Find the Value of y

Substitute z = 5 in equation (5):

y = ^{14 − 4(5)}/₃

y = ^{14 − 20}/₃

y = −2

Final Answer

∴ The solution of the given system of equations is:

x = ¹/₅ 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 (1/5, −2).