Answer:
The equation which has infinite many solutions is:
Option: C
C. \(5.1+2y+1.2=-2+2y+8.3\)
Step-by-step 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:
\(-6.8+2.4+3y=4.3-3y\\\\i.e.\\\\-4.4+3y=4.3-3y\\\\i.e.\\\\3y+3y=4.3+4.4\\\\i.e.\\\\6y=8.7\\\\y=\dfrac{8.7}{6}\\\\i.e.\\\\y=1.45\)
Hence, we get a unique solution.
B)
\(\dfrac{1}{3}y+2.5-\dfrac{2}{3}y=1.2\)
On solving this equation:
\(\dfrac{1}{3}y-\dfrac{2}{3}y=1.2-2.5\\\\i.e.\\\\\dfrac{-1}{3}y=-1.3\\\\i.e.\\\\y=1.3\times 3\\\\i.e.\\\\y=3.9\)
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)
\(\dfrac{2}{5}y=2.3+\dfrac{3}{2}y\)
i.e.
\(\dfrac{2}{5}y-\dfrac{3}{2}y=2.3\\\\i.e.\\\\\dfrac{2\times 2-3\times 5}{10}y=2.3\\\\i.e.\\\\\dfrac{4-15}{10}y=2.3\\\\i.e.\\\\\dfrac{-11}{10}y=2.3\\\\i.e.\\\\y=\dfrac{2.3\times 10}{-11}\\\\i.e.\\\\y=\dfrac{23}{-11}\\\\i.e.\\\\y=-2.0909\)
Hence, again we get a unique solution.
