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

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

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Solution

Equation are written as

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

If a system of linear equations has infinite number of solutions then the condition is a₁/a₂=b₁/b₂=c₁/c₂
$\frac{2 a - 1}{3}$ = $\frac{3}{b - 1}$ = $\frac{5}{2}$
$\frac{2 a - 1}{3}$ = $\frac{5}{2}$
4a-2=15
a= $\frac{17}{4}$

$\frac{3}{b - 1}$ = $\frac{5}{2}$
6=5b-5
11=5b
b= $\frac{11}{5}$

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

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

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