How can you tell how many solutions an equation has without solving?

Correct answer:

The coefficients are the numbers alongside the variables. The constants are the numbers alone with no variables. If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur.

How do you know if a solution has many solutions?

Some equations have infinitely many solutions. In these equations, any value for the variable makes the equation true. You can tell that an equation has infinitely many solutions if you try to solve the equation and get a variable or a number equal to itself. Combine like terms 2x and 2x.

How do you tell if an equation has 1 or 2 solutions?

If you end up with the variable equal to a number it’s one solution, if you end up with a number equal to itself it’s an identity and there are infinite solutions and if you end up with a false statement then there is no solution.

How many solutions does the system have?

A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line).

How do you find all the solutions of an equation?

How do you know how many solutions a quadratic equation has?

Solution:
  1. if the discriminant is positive , then the quadratic equation has two solutions.
  2. if the discriminant is equal , then the quadratic equation has one solution.
  3. if the discriminant is negative , then the quadratic equation has no solution.

What does infinitely many solutions look like?

We can identify which case it is by looking at our results. If we end up with the same term on both sides of the equal sign, such as 4 = 4 or 4x = 4x, then we have infinite solutions. If we end up with different numbers on either side of the equal sign, as in 4 = 5, then we have no solutions.