Solution to a System

Front

What is a solution to a system of equations?

Back

A solution to a system of equations is an ordered pair (x, y) that satisfies all equations in the system.

Front

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

Back

A point is a solution if its (x, y) coordinates satisfy both equations in the system.

Front

What does it mean if two equations have the same solution?

Back

It means that the lines represented by the equations intersect at that point.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of the lines of each equation plotted on a coordinate plane.

Front

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

Back

The intersection point represents the solution to the system of equations.

Front

What is an ordered pair in the context of systems of equations?

Back

An ordered pair is a pair of numbers (x, y) that represents a point on the coordinate plane.

Front

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

Back

It means that the lines are parallel and do not intersect.

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 do you check if a specific point is a solution to a system of equations?

Back

Substitute the x and y values of the point into both equations and see if both equations are true.

Front

What is the first step in solving a system of equations graphically?

Back

The first step is to graph each equation on the same coordinate plane.