Algebra II - No Real Solutions Vocabulary

Vocabulary flashcards covering real numbers, equations, systems of equations, and algebraic proofs for systems with no real solutions.

Real number

Any number that can be expressed on a number line that spans from negative infinity to positive infinity.

Solution

A value that replaced a variable that makes an equation true.

System

A collection of equations that contain the same variables.

Solution to a system of equations

Only values that make all of the equations true in the system at the same time are considered solutions.

No real solutions

Means that there are no real values that make all of the equations in a system true simultaneously.

Algebraic method for testing system solutions

Substituting one equation into the other and analyzing the results; for example, setting $y = x + 3$ and $y = x + 1$ equal as $x + 3 = x + 1$ yields the false statement $3 = 1$, showing no solution exists.

Mathematical Practice Standard

Look for and express regularity in repeated reasoning.