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

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

Step-by-step 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 $3x-2y=8$ )

$32=2a$

$\frac{32}{32}=\frac{2a}{32}$

$1=\frac{a}{16}$

$1\times 16=\frac{a}{16}\times 16$

$16=a$

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