Question

The pair of equation 2x+3y=5 and 4x+6y=15 has ____ a) a unit solution b) exactly two solution c) infinitely many solution d) no solution

Answer 1

Given:

2x+3y=5

4x+6y=15

To find:

The number of solutions of the given equation.

Solution:

1)The given equations are the linear equation in two variables which can be noted in the form.

a1x+b1y+c1=0

a2x+b2y+c2=0

2)If,

• a1/a2 = b1/b2 = c1/c2 [Concurrent lines]

Infinite many soutions.

• a1/a2 = b1/b2 ≠ c1/c2 [parallel lines]

No solution

• a1/a2 ≠ b1/b2 ≠ c1/c2 [intersecting lines]

Two solutions.

3)As per the equations given in the question then the ratio of the its coefficients

• 2/4 = 3/6 ≠ 5/15

• 1/2 = 1/2 ≠ 1/3

4)The given pair of equation are of parallel line which have no solution.

Answer is (D) No solution.