Question

If the system of equations kx – 5y = 2, 6x + 2y = 7 has no solution, then k =
A. – 10
B. – 5
C. – 6
D. – 15

Answer 1

||✪✪ QUESTION ✪✪||

If the system of equations kx – 5y = 2, 6x + 2y = 7 has no solution, then k =

A. – 10

B. – 5

C. – 6

D. – 15

|| ★★ 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 ✰✰ ||

→ kx - 5y - 2 = 0 = a1x + b1y + c1 = 0

→ 6x + 2y - 7 = 0 = a2x + b2y + c2 = 0

we get,

→ a1 = k , b1 = (-5) , c1 = (-2)

→ a2 = 6 , b2 = 2 , c2 = (-7)

As, we have to Find value of k , so that, the system will have no solution.

So,

Both the straight lines will be parallel if and ,

a1/a2 = b1/b2 ≠ c1/c2

Putting values we get,

→ k / 6 = (-5/2) ≠ (-2) /(-7)

→ k/6 = (-5) /2 ≠ 2/7

Comparing first two ,

→ k/6 = (-5/2)

cross - Multiplying,

→ 2k = 6*(-5)

→ 2k = (-30)

Dividing both sides by 2 now,

→ k = (-15)

Hence, we can say that, value of k will be (-15) Option(D), So, that, The Equations have No solution.

Answer 2

Step-by-step explanation:

$\huge\underline{\sf Your\:Answer}$

Refer to the attached picture

Value of K will be —15 then the equations have no solution