# Find the Values of a and B for Which the Following System of Equations Has Infinitely Many Solutions: (2a - 1)X - 3y = 5 3x + (B - 2)Y = 3 - Mathematics

Find the values of a and b for which the following system of equations has infinitely many solutions:

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

3x + (b - 2)y = 3

#### Solution

The given system of equations is

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

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

It is of the form

a_1x + b_1y + c_1 = 0

a_2x + b_2y + c_2 = 0

Where a_1 = 2a - 1, b_1 = -3,c_1 = -5

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

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 - 2) = (-5)/(-3)

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

=> (3(2a - 1))/3 = 5 and -9 = 5(b - 2)

=> 2a = 5 + 1 and -9 + 10 = 5b

=> a = 6/2 and 1 = 5b

=> a= 3 and 1/5 = b

=> a = 3 and b = 1/5

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

if a = 3 and b = 1/5

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.5 | Q 36.1 | Page 75