Question

HELP PLEASE

Which equation has infinitely many solutions?
A) -6.8+3y+2.4=4.3-3y
B)1/3y+2.5-2/3y=1.2
C)5.1+2y+1.2=-2+2y+8.3
D)2/5y=2.3+3/2y

Answer 1

when the answer is 0/0 the equation has infinite solutions

Answer 2

The equation which has infinite many solutions is:

Option: C

C.
`5.1+2y+1.2=-2+2y+8.3`

Explanation:

An equation is said to have infinite many solution if the equation holds true for infinite many values of y.

A)

`-6.8+3y+2.4=4.3-3y`

On solving for the equation we have:

`-6.8+2.4+3y=4.3-3y\\\\i.e.\\\\-4.4+3y=4.3-3y\\\\i.e.\\\\3y+3y=4.3+4.4\\\\i.e.\\\\6y=8.7\\\\y=(8.7)/(6)\\\\i.e.\\\\y=1.45`

Hence, we get a unique solution.

B)

`(1)/(3)y+2.5-(2)/(3)y=1.2`

On solving this equation:

`(1)/(3)y-(2)/(3)y=1.2-2.5\\\\i.e.\\\\(-1)/(3)y=-1.3\\\\i.e.\\\\y=1.3* 3\\\\i.e.\\\\y=3.9`

Hence, we get a unique solution.

C)

`5.1+2y+1.2=-2+2y+8.3\\\\i.e.\\\\5.1+1.2+2y=-2+8.3+2y\\\\i.e.\\\\6.3+2y=6.3+2y`

Hence, the equation is true for infinite many values of y.

Hence, the equation has infinite many solution.

D)

`(2)/(5)y=2.3+(3)/(2)y`

i.e.

`(2)/(5)y-(3)/(2)y=2.3\\\\i.e.\\\\(2* 2-3* 5)/(10)y=2.3\\\\i.e.\\\\(4-15)/(10)y=2.3\\\\i.e.\\\\(-11)/(10)y=2.3\\\\i.e.\\\\y=(2.3* 10)/(-11)\\\\i.e.\\\\y=(23)/(-11)\\\\i.e.\\\\y=-2.0909`

Hence, again we get a unique solution.