When you solve a linear equation how do you recognize if the equation has 1 solution no
solution, or infinite solution?

If you solve a linear equation you have two different lines.

Now with that being said the solutions are as follows;

One Solution: The slopes are different

No solution: The slopes are the same and the y intercepts are different

Infinite Solutions: The slopes are the same and the y intercepts are different

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.