Q. 84.0( 4 Votes )

# If the system of A. a = 2b

B. b = 2a

C. a + 2b = 0

D. 2a + b = 0

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) and solving the extreme left and extreme right portion of the equality we get the value of a

### ⇒ 14a = 56 ⇒ a = 4

### We now put the value of a and solve for b

### ⇒ ⇒ a + b = 12⇒ b = 8

### So b = 2a

__The__ __correct relationship between a & b for which the system of equations has infinitely many solution is b = 2a__

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