Determine the values of a and b so that the following system of linear equations have infinitely many solutions :

(2a − 1) x + 3y − 5 = 0
3x + (b − 1)y − 2 = 0

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Solution

GIVEN:

To find: To determine for what value of k the system of equation has infinitely many solutions

We know that the system of equations

For infinitely many solution

Here

Again consider

Hence for and the system of equation has infinitely many solution.

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Similar questions

Determine the values of a and b so that the following system of linear equations have infinitely many solutions:

(2a - 1) x + 3y - 5 = 0

3x + (b-1) y - 2 = 0

(2 a - 1) x - 3 y = 5

3 x + (b - 2) y = 3

(2 a - 1) x + 3 y = 5, 3 x + (b - 1) y = 2 .

(2 m - 1) x + 3 y = 5; 3 x + (n - 1) y = 2

(3 k + 1) x + 3 y - 2 = 0

(k^{2} + 1) x + (k - 2) y - 5 = 0

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