Find the Solution of the Pair of Equations and Hence Find λ

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question: Find the solution of the pair of equations

x/10 + y/5 − 1 = 0  …… (1)

x/8 + y/6 = 15  …… (2)

Hence find λ if y = λx + 5.

Step 1: Simplify the Given Equations

Equation (1):

x/10 + y/5 = 1

Multiply both sides by 10:

x + 2y = 10  …… (3)

Equation (2):

Multiply both sides by 24:

3x + 4y = 360  …… (4)

Step 2: Solve the Equations (3) and (4)

Multiply equation (3) by 3:

3x + 6y = 30  …… (5)

Subtract equation (4) from equation (5):

(3x + 6y) − (3x + 4y) = 30 − 360

2y = −330

⇒ y = −165

Step 3: Find the Value of x

Substitute y = −165 in equation (3):

x + 2(−165) = 10

x − 330 = 10

⇒ x = 340

Step 4: Find the Value of λ

Given:

y = λx + 5

Substitute x = 340 and y = −165:

−165 = λ(340) + 5

λ(340) = −170

⇒ λ = −¹/₂

Final Answer

∴ The solution of the given pair of equations is:

x = 340 and y = −165

and the value of λ = −¹/₂

Conclusion

Thus, by solving the given pair of linear equations and substituting the values in y = λx + 5, we find that the value of λ is −1/2.