Question

Which equation has no solution?

Answer 1

C. Because 7y -7y = -15
0 = -15

Answer 2

Answer:

The equation which has no solution is:

                           Option: C

           c)     $7y+9=7y-6$    

Step-by-step explanation:

The equation is said to have a no solution if we get a false identity on solving the equation.

a)

$5m-6=5m+7-m$

On combining the like terms in the right hand side of the equation we have:

$5m-6=5m-m+7\\\\5m-6=4m+7\\\\5m-4m=7+6\\\\m=13$

Hence, we get a unique solution to the equation.

b)

$3w+4-w=5w-2(2w-2)$

on using the distributive property in the right hand side of the equation we have:

$3w+4-w=5w-2\times w-2\times (-2)\\\\3w-w+4=5w-2w+4\\\\2w+4=3w+4\\\\3w-2w=4-4\\\\w=0$

Again we get a unique solution to the equation.

c)

$7y+9=7y-6$

on subtracting 7y from both the sides of the equation we have:

$7y-7y-6=9\\\\-6=9$

which is a false identity.

Hence, the equation has no solution.

d)

$4z+8=-4z-2\\\\i.e.\\\\4z+4z=-2-8\\\\8z=-10\\\\z=\dfrac{-10}{8}\\\\z=\dfrac{-5}{4}$

This equation has a unique solution.