The equation which has infinite many solutions is:
Option: C
C. [tex]5.1+2y+1.2=-2+2y+8.3[/tex]
An equation is said to have infinite many solution if the equation holds true for infinite many values of y.
A)
[tex]-6.8+3y+2.4=4.3-3y[/tex]
On solving for the equation we have:
[tex]-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[/tex]
Hence, we get a unique solution.
B)
[tex]\dfrac{1}{3}y+2.5-\dfrac{2}{3}y=1.2[/tex]
On solving this equation:
[tex]\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[/tex]
Hence, we get a unique solution.
C)
[tex]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[/tex]
Hence, the equation is true for infinite many values of y.
Hence, the equation has infinite many solution.
D)
[tex]\dfrac{2}{5}y=2.3+\dfrac{3}{2}y[/tex]
i.e.
[tex]\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[/tex]
Hence, again we get a unique solution.
