Question

find out the value of c which the pair of equations cx-y=2 and 6x-2y=4 will have infinitely many solutions
(a) 3
(b) -3
(c) -12
(d) 4​

Answer 1

Answer:

Option a : 3

Step-by-step explanation:

Given:

Two equations:

• cx - y = 2
• 6x - 2y = 4

To Find:

• The value of c so that the the pair of equations will have infinitely many solutions.

Solution:

Here we are given two equations

cx - y = 2 and

6x - 2y = 4

We have to find the value of c so that the number of solutions for the pair of equations is infinite.

We know that if a pair of equations have infinite number of solutions,

$\sf{\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}}$

where a₁ = c, a₂ = 6, b₁ = -1, b₂ = -2, c₁ = 2, c₂ = 4

Substitute the data,

$\sf{\dfrac{c}{6} =\dfrac{-1}{-2}=\dfrac{2}{4} }$

Equating the first part,

c/6 = -1/-2

-6 = -2c

2c = 6

c = 6/2

c = 3

Equating the second part,

c/6 = 2/4

4c = 12

c = 12/4

c = 3

Hence the value of c so that the equations have infinite solution is 3.

Therefore option a is correct.

Notes:

If a pair of equations have a unique solution and is consistent,

$\sf{\dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2} }$

If a pair of equations have infinite number of solutions and is consistent,

$\sf{\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}}$

If a pair of equations have no solution and is inconsistent,

$\sf{\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2}}$