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# 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 - CBSE Class 10 - Mathematics

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ConceptPair of Linear Equations in Two Variables

#### Question

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

#### Solution

The given system of equations may be written as

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

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

It is of the form

a_1x + b_1y + c_1 = 0

a_2x + b_2y + c_2 = 0

Where a_1 = 2a, b_1 = 3, c_1 = -5

And a_2 = 3, b_2 = b - 1, c_2 = -2

The given system of equations will have infinite number of solutions, if

a_1/a_2 - b_1/b_2 = c_1/c_2

=> (2a - 1)/3 = 3/(b - 1) = (-5)/(-2)

=> 2(2a - 1) = (-5)/(-2)  and 3/(b -1) = (-5)/(-2)

=> 2(2a - 1) = 5 xx 3 and 3 xx 2 = 5(b - 1)

=> 4a - 2 = 15 and  6 = 5b - 5

=> 4a = 15 + 2 and 6 + 5 = 5b

=> a = 17/4 and 11/5 = b

=> a = 17/4 and b = 11/5

Hence, the given system of equations will have infinitely many solutions

if a = 17/4 and b = 11/5

Is there an error in this question or solution?

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Solution 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 Concept: Pair of Linear Equations in Two Variables.
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