Find the values of a and b for which the following system of linear equations has infinite number of solutions :

$2 x - 3 y = 7 (a + b) x - (a + b - 3) y = 4 a + b$

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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

Consider the following

5a − 4b + 21 = 0……(1)

Again

a + b + 6 = 0…… (2)

Multiplying eq. (2) by 4 and adding eq. (1)

Putting the value of a in eq. (2)

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

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Similar questions

2 x - 3 y = 7, (a + b) x - (a + b - 3) y = 4 a + b .

a

b

2 x - 3 y = 7

(a + b) x - (a + b - 3) y = 4 a + b

2 x + 3 y = 7 (a + b) x + (2 a - b) y = 21

2 x - 3 y = 7

(a + b) x - (a + b - 3) y = 4 a + b

Find the values of A and B for which the following pair of linear equations infinitely many solutions:

2x+3y=7

(a+b)x+(2a-b)y=21

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