Question

in the system of linear equation 7x-5y=2 and 2x+ky=5, find the value of k or the condition of k for which the given system of liner equations has a unique solution.​

Answer 1

Step-by-step explanation:

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Answer 2

Question:

In the system of linear equations 7x - 5y = 2 and 2x + ky = 5, find the value of k or the condition of k for which the given system of liner equations has a unique solution.

Answer:

All real values except -10/7 .

Note:

• 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.

Solution:

The given system of linear equations in two variables is ; 7x - 5y = 2 and 2x + ky = 5.

OR

7x - 5y - 2 = 0

2x + ky - 5 = 0

Here ,

a1 = 7

a2 = 2

b1 = -5

b2 = k

c1 = -2

c2 = -5

Now,

For unique solution , a1/a2 ≠ b1/b2

=> 7/2 ≠ -5/k

=> k ≠ -5•(2/7)

=> k ≠ -10/7

Thus,

For unique solution, k can take any real value except -10/7 .