Answer:
The equation which has no solution is:
Option: C
c) [tex]7y+9=7y-6[/tex]
Step-by-step explanation:
The equation is said to have a no solution if we get a false identity on solving the equation.
a)
[tex]5m-6=5m+7-m[/tex]
On combining the like terms in the right hand side of the equation we have:
[tex]5m-6=5m-m+7\\\\5m-6=4m+7\\\\5m-4m=7+6\\\\m=13[/tex]
Hence, we get a unique solution to the equation.
b)
[tex]3w+4-w=5w-2(2w-2)[/tex]
on using the distributive property in the right hand side of the equation we have:
[tex]3w+4-w=5w-2\times w-2\times (-2)\\\\3w-w+4=5w-2w+4\\\\2w+4=3w+4\\\\3w-2w=4-4\\\\w=0[/tex]
Again we get a unique solution to the equation.
c)
[tex]7y+9=7y-6[/tex]
on subtracting 7y from both the sides of the equation we have:
[tex]7y-7y-6=9\\\\-6=9[/tex]
which is a false identity.
Hence, the equation has no solution.
d)
[tex]4z+8=-4z-2\\\\i.e.\\\\4z+4z=-2-8\\\\8z=-10\\\\z=\dfrac{-10}{8}\\\\z=\dfrac{-5}{4}[/tex]
This equation has a unique solution.
