Question

for which value of k, 2x+3y=1 and (k-1)x+(2k+1)y=k-1 has no solution.

Answer 1

hope it will help you

Answer 2

Concept:

A two-variable linear equation is one with the formula ax + by + c = 0, where a, b, c  ∈ R, a, and b  not equal to 0. An inconsistent pair of linear equations is a system of linear equations that cannot be solved. By comparing the coefficients of the equations in a system of linear equations, we can determine whether the system of equations has no solution.

Given:

The given set of equations 2x + 3y = 1 and (k - 1)x + (2k + 1)y = k - 1

Find:

We have to find the value of x for no solution system of equations.

Solution:

Let's take the equation as :

2x + 3y = 1 .. (1)

(k - 1)x + (2k + 1)y = k - 1 .. (2)

As we know that if a system has no solution, then

a1/a2 = b1/b2 ≠ c1/c2

Here, a1 = 2, a2 = k - 1, b1 = 3, b2 = 2k + 1, c1 = 1, c2 = k - 1

So, 2/ (k - 1) = 3/ 2k + 1

2(2k + 1) = 3(k - 1)

4k + 1 = 3k - 3

k = -5

Hence, the value of k is -5.

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