solve the equation and state if it an identity ( all real numbers) or a contradiction(no solution)

5x+6+6x=10x+6+y

You cannot solve a single equation with two unknowns. The 6's cancel each other out.

11x = 10x + y

x and y can have any same value.

To solve the equation, we need to simplify and combine like terms on both sides of the equation. Let's go through the steps:

5x + 6 + 6x = 10x + 6 + y

Combining like terms, we have:

11x + 6 = 10x + 6 + y

Rearranging the terms, we get:

11x - 10x - y = 6 - 6

Simplifying further, we have:

x - y = 0

This equation represents a line in the xy-plane where every point on the line satisfies the equation. Therefore, it is an identity since it holds true for all real numbers.

In summary, the solution to the equation 5x + 6 + 6x = 10x + 6 + y is x - y = 0, and it is an identity.