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One equation of a pair of dependent linear equations is -5x + 7y = 2. The second equation can be
a. 10x + 14y + 4 = 0
b. -10x - 14y + 4 = 0
c. -10x + 14y + 4 = 0
d. 10x - 14y = -4

Solution:

Given, one equation of a pair of dependent linear equations is -5x + 7y = 2.

We have to find the second equation.

A pair of linear equations in two variables be a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 is is dependent and consistent,if \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}\)

Here, a₁ = -5, b₁ = 7, c₁ = -2

From the options,

A) 10x + 14y + 4 = 0

a₂ = 10, b₂ = 14, c₂ = 4

So, a₁/a₂ = -5/10 = -1/2

b₁/b₂ = 7/14 = 1/2

c₁/c₂ = -2/4 = -1/2

So, \(\frac{a_{1}}{a_{2}}\neq \frac{b_{1}}{b_{2}}\neq \frac{c_{1}}{c_{2}}\)

Therefore, option A is false.

B) -10x - 14y + 4 = 0

a₂ = -10, b₂ = -14, c₂ = 4

So, a₁/a₂ = -5/-10 = 1/2

b₁/b₂ = 7/-14 = -1/2

c₁/c₂ = -2/4 = -1/2

So, \(\frac{a_{1}}{a_{2}}\neq \frac{b_{1}}{b_{2}}\neq \frac{c_{1}}{c_{2}}\)

Therefore, option B is false.

C) -10x + 14y + 4 = 0

a₂ = -10, b₂ = 14, c₂ = 4

So, a₁/a₂ = -5/-10 = 1/2

b₁/b₂ = 7/14 = 1/2

c₁/c₂ = -2/4 = -1/2

So, \(\frac{a_{1}}{a_{2}}= \frac{b_{1}}{b_{2}}\neq \frac{c_{1}}{c_{2}}\)

Therefore, option C is false.

D) 10x - 14y = -4

a₂ = 10, b₂ = -14, c₂ = 4

So, a₁/a₂ = -5/10 = -1/2

b₁/b₂ = 7/-14 = -1/2

c₁/c₂ = -2/4 = -1/2

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

Therefore, option D is true.

Therefore, the second equation is 10x - 14y + 4 = 0.

✦ Try This: One equation of a pair of dependent linear equations is 3x + 7y = 6. The second equation can be
a. 6x + 14y = 12
b. 7x + 12y = 8
c. 13x + y = 5
d. 14x + 7y = 8

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

NCERT Exemplar Class 10 Maths Exercise 3.1 Problem 9

One equation of a pair of dependent linear equations is -5x + 7y = 2. The second equation can be, a. 10x + 14y + 4 = 0, b. -10x - 14y + 4 = 0, c. -10x + 14y + 4 = 0, d. 10x - 14y = -4

Summary:

One equation of a pair of dependent linear equations is -5x + 7y = 2. The second equation can be 10x - 14y = -4.

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