Determining the Number of Solutions to a System Algebraically
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Determining the Number of Solutions to a System Algebraically
Algebraically trying to solve a system of linear-quadratic or quadratic-quadratic equations with no real solution results in the square root of a negative number or a false statement. The square root of a negative number is not a real value, and a false statement tells you that there are no values for the variables that satisfy both equations.
Algebraically trying to solve a system of linear-quadratic or quadratic-quadratic equations with an infinite number of real solutions results in a true statement, where the two sides of the equation are equal for any real variable value. The true statement tells you that any variable value that satisfies one equation will also satisfy the other.