Question

the pair of equation 2 X + 3 y = 5 and 4 x +6y=15 has how many solutions​

Answer 1

Answer:

Option (C) No Solution

Step-by-step explanation:

The pair of equation has no solution.

Explanation:

The given pair of equations are :2x + 3y = 52x+3y=5 (1)

and 4x + 6y = 154x+6y=15 . (2)

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

\dfrac{2}{4}=\dfrac{1}{2}

4

2

=

2

1

(i)

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

\dfrac{3}{6}=\dfrac{1}{2}

6

3

=

2

1

(ii)

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

\dfrac{5}{15}=\dfrac{1}{3}

15

5

=

3

1

(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