Solve the System of 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:

44/(x + y) + 30/(x − y) = 10  …… (1)

55/(x + y) + 40/(x − y) = 13  …… (2)

Step 1: Substitute (x + y) = a and (x − y) = b

Let x + y = a and x − y = b

Then equations (1) and (2) become:

44/a + 30/b = 10  …… (3)

55/a + 40/b = 13  …… (4)

Step 2: Remove Fractions

Multiply equation (3) by ab:

44b + 30a = 10ab  …… (5)

Multiply equation (4) by ab:

55b + 40a = 13ab  …… (6)

Step 3: Solve the Equations

Multiply equation (5) by 4:

176b + 120a = 40ab  …… (7)

Multiply equation (6) by 3:

165b + 120a = 39ab  …… (8)

Subtract equation (8) from equation (7):

(176b − 165b) = (40ab − 39ab)

11b = ab

⇒ a = 11

Step 4: Find the Value of b

Substitute a = 11 in equation (5):

44b + 30(11) = 10(11)b

44b + 330 = 110b

66b = 330

⇒ b = 5

Step 5: Find the Values of x and y

We have:

x + y = 11  …… (9)

x − y = 5  …… (10)

Add equations (9) and (10):

2x = 16

⇒ x = 8

Substitute x = 8 in equation (10):

8 − y = 5

⇒ y = 3

Final Answer

∴ The solution of the given system of equations is:

x = 8 and y = 3

Conclusion

Thus, by substituting x + y = a and x − y = b and using the substitution method, we find that the solution of the given system of equations is (8, 3).