Question: Anywhere I've looked, the definition of solution of equation is root(s) of that equation. But why does a textbook say that equation $y=7-3x$ has infinite number of solutions?

Thanks

Answer: 
Equations have solutions, but not roots. Polynomials have roots, but not solutions.

* The equation $y=7-3x$ has infinitely many solutions.
* The equation $0=7-3x$ has only one solution.
* The polynomial $7-3x$ has only one root, which is the solution of the equation $0=7-3x$.
This is because a root is just setting the y value equal to 0 and solving for x, whereas the equation itself is just saying "how many points are there such that y = 7 - 3x", not "how many points are there such that the y value is 0". For example, (2, 1) would be a solution to this equation, but not a root.

Hope this helps!