A day full of math games & activities. Find one near you.

For the pair of equations λx + 3y = -7; 2x + 6y = 14 to have infinitely many solutions, the value of λ should be 1. Is the statement true?

Solution:

Given, the pair of linear equations is

λx + 3y = -7

2x + 6y = 14

We have to determine if λ is 1 the pair of equations has infinitely many solutions.

We know that,

For a pair of linear equations in two variables be a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0,

If \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}\), then

i) the pair of linear equation is dependent and consistent

ii) the graph will be a pair of coincident lines. Each point on the lines will be a solution and so the pair of equations will have infinitely many solutions.

Here, a₁ = λ, b₁ = 3, c₁ = -7

a₂ = 2, b₂ = 6, c₂= 14

So, a₁/a₂= λ/2

b₁/b₂ = 3/6 = 1/2

c₁/c₂ = -7/14 = -1/2

Case a) λ/2 = 1/2

λ = 2/2

λ = 1

Case b) λ/2 = -1/2

λ = -2/2

λ = -1

The value of λ is not constant.

Therefore, the pair of equations to have infinitely many solutions the value of λ should not be 1.

✦ Try This: For the pair of equations λx + 2y = 7; 2x + 4y = 14 to have infinitely many solutions, the value of λ should be 1. Is the statement true?

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3

NCERT Exemplar Class 10 Maths Exercise 3.2 Problem 4

For the pair of equations λx + 3y = -7; 2x + 6y = 14 to have infinitely many solutions, the value of λ should be 1. Is the statement true?

Summary:

For the pair of equations λx + 3y = -7; 2x + 6y = 14 to have infinitely many solutions, the value of λ should be 1. The statement is not true.

☛ Related Questions: