Question

The pair of equations 2x + 3y = 5 and 4x + 6y = 15 have
(A) unique solution
(B) infinitely many solutions
no solution
(D) none of these​

Answer 1

 (C) no solution

The pair of equation  has no solution.

Explanation:

The given pair of equations are :$2x + 3y = 5$           (1)

and $4x + 6y = 15$.                                                       (2)

The ratio of the coefficient of x of the equation (1) to equation (2) is

$\dfrac{2}{4}=\dfrac{1}{2}$            (i)

The ratio of the coefficient of y of the equation (1) to equation (2) is

$\dfrac{3}{6}=\dfrac{1}{2}$                (ii)

The ratio of the constant term of the equation (1) to equation (2) is

$\dfrac{5}{15}=\dfrac{1}{3}$        (iii)

From (i) , (ii) and (iii).

The ratio of the coefficient of x is equal to the ratio of coefficient of y but not equal to the ratio of the constant terms.

It means the pair of equation are inconsistent and they representing parallel lines with no solution.

[Note : For unique solution : Ratio of the coefficient of x is not equal to the ratio of coefficient of y

For infinitely many solution : Ratio of the coefficient of x is not equal to the ratio of coefficient of y is equal to the ratio of corresponding constant terms]

Hence, the correct option is  (C)no solution

# Learn more :

The equations 2x+3y-5=0 and 6y-4x=10 when solved simultaneously have-

A) only one solution

B) no solution

C) only two solutions

D) infinite number of solutions

https://brainly.in/question/6228889

Answer 2

Answer:

Step-by-step explanation:

The given pair of equations are :           (1)

and .                                                       (2)

The ratio of the coefficient of x of the equation (1) to equation (2) is

           (i)

The ratio of the coefficient of y of the equation (1) to equation (2) is

               (ii)

The ratio of the constant term of the equation (1) to equation (2) is

       (iii)

From (i) , (ii) and (iii).

The ratio of the coefficient of x is equal to the ratio of coefficient of y but not equal to the ratio of the constant terms.

It means the pair of equation are inconsistent and they representing parallel lines with no solution.

[Note : For unique solution : Ratio of the coefficient of x is not equal to the ratio of coefficient of y

For infinitely many solution : Ratio of the coefficient of x is not equal to the ratio of coefficient of y is equal to the ratio of corresponding constant terms]

Hence, the correct option is  (C)no solution

# Learn more :

The equations 2x+3y-5=0 and 6y-4x=10 when solved simultaneously have-

A) only one solution

B) no solution

C) only two solutions

D) infinite number of solutions

brainly.in/question/6228889