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:

3/x − 1/y = −9  …… (1)

2/x + 3/y = 5  …… (2)

Step 1: Substitute 1/x = a and 1/y = b

Let 1/x = a and 1/y = b

Then equations (1) and (2) become:

3a − b = −9  …… (3)

2a + 3b = 5  …… (4)

Step 2: Express One Variable in Terms of the Other

From equation (3):

3a − b = −9

⇒ b = 3a + 9  …… (5)

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

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

2a + 3(3a + 9) = 5

2a + 9a + 27 = 5

11a = −22

⇒ a = −2

Step 4: Find the Value of b

Substitute a = −2 in equation (5):

b = 3(−2) + 9

b = −6 + 9

b = 3

Step 5: Find the Values of x and y

Since a = 1/x,

1/x = −2 ⇒ x = −¹/₂

Since b = 1/y,

1/y = 3 ⇒ y = ¹/₃

Final Answer

∴ The solution of the given system of equations is:

x = −¹/₂ and y = ¹/₃

Conclusion

Thus, by substituting 1/x = a and 1/y = b and using the substitution method, we find that the solution of the given system of equations is (−1/2, 1/3).