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:

2/x + 5/y = 1  …… (1)

60/x + 40/y = 19  …… (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:

2a + 5b = 1  …… (3)

60a + 40b = 19  …… (4)

Step 2: Express One Variable in Terms of the Other

From equation (3):

2a = 1 − 5b

⇒ a = ^{1 − 5b}/₂  …… (5)

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

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

60( ^{1 − 5b}/₂ ) + 40b = 19

30(1 − 5b) + 40b = 19

30 − 150b + 40b = 19

30 − 110b = 19

110b = 11

⇒ b = ¹/₁₀

Step 4: Find the Value of a

Substitute b = ¹/₁₀ in equation (5):

a = ^{1 − 5(1/10)}/₂

a = ^{1 − 1/2}/₂

a = ^1/2/₂

a = ¹/₄

Step 5: Find the Values of x and y

Since a = 1/x,

1/x = ¹/₄ ⇒ x = 4

Since b = 1/y,

1/y = ¹/₁₀ ⇒ y = 10

Final Answer

∴ The solution of the given system of equations is:

x = 4 and y = 10

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 (4, 10).