Question

For what value of a would the following system of equations have an infinite number of solutions? 3x - 2y = 8 and 12x - 8y = 2a

Answer 1

The value of "a" in the given system of equations is 16

Therefore a=16

Therefore substitute a=16 then equation (2) becomes

12x-8y=2(16)

12x-8y=32

Explanation:

Given system of equations are
`3x-2y=8\hfill (1)`

and
`12x-8y=2a\hfill (2)` have infinite number of solutions

To find the value of a in the given system of equations :

From given the equations have infinite number of solutions and so they refers the same line

Therefore the equation (2) becomes

`12x-8y=2a`

`4(3x-2y)=2a`

`4(8)=2a` ( by
`3x-2y=8` )

`32=2a`

`(32)/(32)=(2a)/(32)`

`1=(a)/(16)`

`1* 16=(a)/(16)* 16`

`16=a`

Rewritting the above equation we get

`a=16`

The value of "a" in the given system of equations is 16

Therefore a=16

Therefore equation (2) becomes

12x-8y=2(16)

12x-8y=32