Alg 2 Flashcard 4

Front

What is a solution to a system of equations?

Back

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

Front

How do you determine if a point is a solution to an equation?

Back

Substitute the x and y values of the point into the equation. If the equation holds true, then it is a solution.

Front

What does it mean if two equations have no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What does it mean if two equations have infinite solutions?

Back

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

Front

What is the graphical representation of a system with one solution?

Back

The lines intersect at exactly one point.

Front

What is the graphical representation of a system with no solution?

Back

The lines are parallel and do not intersect.

Front

What is the graphical representation of a system with infinitely many solutions?

Back

The lines overlap completely, representing the same line.

Front

How can you tell if a point is a solution to a system of equations?

Back

Check if the point satisfies all equations in the system.

Front

What is the significance of the point (1, 0) in a system of equations?

Back

It is a solution to the system if it satisfies all equations.

Front

What does it mean for a system of equations to have one solution?

Back

There is exactly one set of values for the variables that satisfies all equations.