CA HW Flashcard 11.1

Front

What is a solution to a system of equations?

Back

A solution to a system of equations is a set of values for the variables that makes all equations true simultaneously.

Front

What does it mean if a system of equations has no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

What does it mean if a system of equations has exactly one solution?

Back

It means that the equations represent lines that intersect at exactly one point.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

Front

How can you determine the number of solutions in a system of equations graphically?

Back

By graphing the equations and observing the number of intersection points.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is the graphical representation of a system of equations?

Back

It is the visual depiction of the equations on a coordinate plane, showing their relationships and intersections.

Front

What is the significance of the point of intersection in a system of equations?

Back

The point of intersection represents the solution to the system, where all equations are satisfied.

Front

What is a consistent system of equations?

Back

A consistent system has at least one solution, which can be either one solution or infinitely many.