The value of c for which the pair of equations cx - y = 2 and 6x - 2y = 3 will have infinitely many solutions is
a. 3
b. -3
c. -12
d. no value

Solution:

Given, the pair of equations are

cx - y = 2

6x - 2y = 3

We have to find the value of c for which the equations will have 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 = c, b₁ = -1, c₁ = -2

a₂ = 6, b₂ = -2, c₂ = -3

So, a₁/a₂ = c/6

b₁/b₂ = -1/-2 = 1/2

c₁/c₂ = -2/-3 = 2/3

By using the above result,

\(\frac{c}{6}=\frac{1}{2}=\frac{2}{3}\)

Case (i):

\(\frac{c}{6}=\frac{1}{2}\)

On cross multiplication,

2(c) = 6

c = 6/2

c = 3

Case (ii)

\(\frac{c}{6}=\frac{2}{3}\)

On cross multiplication,

3(c) = 2(6)

3c = 12

c = 12/3

c = 4

We observe that the value of c is not constant.

Therefore, there is no value of c for which the given equations will have infinitely many solutions.

✦ Try This: The value of c for which the pair of equations cx - 2y = -2 and 4x - 3y = -3 will have infinitely many solutions is

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

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NCERT Exemplar Class 10 Maths Exercise 3.1 Problem 8

The value of c for which the pair of equations cx - y = 2 and 6x - 2y = 3 will have infinitely many solutions is, a. 3, b. - 3,c. -12, d. no value

Summary:

The value of c for which the pair of equations cx - y = 2 and 6x - 2y = 3 will have infinitely many solutions are of no value

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