215k views
5 votes
For what value of a would the following system of equations have an infinite number of solutions? 3x - 2y = 8 and 12x - 8y = 2a

User Dean Povey
by
6.9k points

1 Answer

4 votes

Answer:

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

User SARI
by
7.0k points