# If the pair of equations 2x + 3y = 7; (a + b)x + (2a – b)y = 21 has infinitely many solutions then find the values of a, b.

Given, 2x + 3y = 7; (a + b)x + (2a – b)y = 21

We know that a pair of linear equations has infinitely many solutions

when,

Here, a1 = 2, b1 = 3, c1 = 7

and a2 = (a + b), b2 = (2a – b), c2 = 21

A + b = 6 …(i)

2a – b = 9 …(ii)

Adding both the equations we get,

3a = 15

a = 5

b = 6 – 5

b = 1

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RELATED QUESTIONS :

Comparing the ratio and find out whether the following pairs of linear equations are consistent or inconsistent.

(i) 2x – 3y = 8; 4x – 6y = 9

(ii) 3x – y = 2; 6x – 2y = 4

(iii) 2x – 2y = 2; 4x – 4y = 5

(iv)

Rajasthan Board Mathematics