Why does my textbook say that equation $y = 7-3x$ has infinite number of solutions while it has only one root?

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 $0=7-3x$.

Solutions are not the same as roots.

A root is a value of $x$ where $y = 0$ and your equation is satisfied. In your equation, the root is $x = 7/3$.

A solution in general is a pair of values $(x,y)$ that satisfy the equation. Examples of solutions to your equation include, but are not limited to, $(7,-14)$, $(0,7)$, and $(\frac 73, 0)$. There are an infinite number of such pairs.

Roots are a special type of solution. But not all solutions are roots.

Tags:

Functions

Analytic Geometry

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