Question

The value of K for which the system of equation 2x + 3y = 5 and 4x + ky = 10 has infinite

number of solutions, is a) 1. b) 3. c) 6 d) 0​

Answer 1

Answer:

The value of k for which the system of equations

2x + 3y = 5

4x + ky = 10

has infinite number of solutions, is

A. 1

B. 3

C. 6

D. 0

|| ★★ FORMULA USED ★★ ||

• A linear equation in two variables represents a straight line in 2D Cartesian plane .

• If we consider two linear equations in two variables, say ;

a1x + b1y + c1 = 0 and

a2x + b2y + c2 = 0

Then ;

✪ Both the straight lines will coincide if ;

a1/a2 = b1/b2 = c1/c2

In this case , the system will have infinitely many solutions.

✪ Both the straight lines will be parallel if ;

a1/a2 = b1/b2 ≠ c1/c2

In this case , the system will have no solution.

✪ Both the straight lines will intersect if ;

a1/a2 ≠ b1/b2

In this case , the system will have an unique solution.

_______________________

|| ✰✰ ANSWER ✰✰ ||

→ 2x + 3y - 5 = 0 = a1x + b1y + c1 = 0

→ 4x + ky - 10 = 0 = a2x + b2y + c2 = 0

we get,

→ a1 = 2 , b1 = 3 , c1 = (-5)

→ a2 = 4 , b2 = k , c2 = (-10)

As, we have to Find value of k , so that, the system will have infinitely many solutions.

So,

Both the straight lines will coincide and,

a1/a2 = b1/b2 = c1/c2

Putting values we get,

→ 2 / 4 = 3/k = (-5) /(-10)

→ 1/2 = 3/k = 1/2

Comparing first two ,

→ 1/2 = 3/k

Cross - Multiply ,

→ k = 2 * 3.

→ k = 6 .

Hence, value of k will be 6 Option (C), So that, The Equations has infinite number of solutions ..

Step-by-step explanation:

Answer 2

2x + 3y = 5 – (1)

4x + ky = 10 – (2)

Multiply (1) by 2 b/s and subtract (2)

4x + 6y - 4x - ky = 10 - 10

6y - ky = 0

6y = ky

k = 6

2x + 3y = 5 – (1')

4x + 6y = 10 – (2')

The equation 0 solutions, because value of none of the variables can be verified.

CHECK:

Multiply (1') by 2 and subtract (2)

4x + 6y - 4x - 6y = 10 - 10

0 = 0