Find the values of a and b for which rach of the following systems of linear equations has an infinite number of equations:

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

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Solution

$2 x + 3 y = 7, (a + b) x + (2 a - b) y = 21.$
A/c to question ,
infinity many solutions possible ,
so,
$\frac{a + b}{2}$ = $\frac{2 a - b}{3}$ = $\frac{21}{7}$

$\frac{a + b}{2}$ = $\frac{21}{7}$ = 3

(a + b) = 6 ------(1)

again,
$\frac{2 a - b}{3}$ = $\frac{21}{7}$ = 3

(2a - b) = 9 --------(2)

solve equations (1) and (2)

3a = 15
a = 5 and b = 1

hence, if a = 5 and b = 1 then , infinitely many solutions possible of given equations.

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Similar questions

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

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

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

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b

2 x - 3 y = 7

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

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