Q. 55.0( 4 Votes )

# Write the set of

Answer :

Given:

Equation 1: 2x + 3y = 7

Equation 2: 2ax + (a + b)y = 28

Both the equations are in the form of :

a_{1}x + b_{1}y = c_{1} & a_{2}x + b_{2}y = c_{2} where

a_{1} & a_{2} are the coefficients of x

b_{1} & b_{2} are the coefficients of y

c_{1} & c_{2} are the constants

__For the system of linear equations to have infinitely many solutions we must have__

………(i)

According to the problem:

a_{1} = 2

a_{2} = 2a

b_{1} = 3

b_{2} = (a + b)

c_{1} = 7

c_{2} = 28

Putting the above values in equation (i) we get:

### …(ii)

### To obtain the value of a & b we need to solve the above equality. First we solve the extreme left and extreme right of the equality to obtain the value of a.

### ⇒ ⇒ 2a*7 = 2*28 ⇒ 14a = 56 ⇒ a = 4

### After obtaining the value of a we again solve the extreme left and middle portion of the equality (ii)

### ⇒ 2*(4 + b) = 3*2*4 ⇒ b + 4 = 12 ⇒ b = 8

__The__ __value of a & b for which the system of equations has infinitely many solution is a = 4 & b = 8__

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