4.10-4.11 Solutions to Systems

Front

What is a solution to a system of equations?

Back

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

Front

How do you represent a solution to a system of equations?

Back

As an ordered pair (x,y) with no spaces, e.g., (3,4).

Front

What does it mean if a point is a solution to a system of equations?

Back

It means that the coordinates of the point satisfy all equations in the system.

Front

How can you verify if a point is a solution to a system?

Back

Substitute the x and y values into each equation; if both equations are true, it is a solution.

Front

What is the graphical method for solving a system of equations?

Back

Graph both equations on the same coordinate plane and identify the point of intersection.

Front

What is an ordered pair?

Back

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

Front

What does it mean if two lines intersect at a point?

Back

It means that the point of intersection is the solution to the system of equations represented by the lines.

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What is the significance of the solution (6,-2) in a system of equations?

Back

It indicates that x=6 and y=-2 satisfy all equations in the system.

Front

What does it mean if a point does not satisfy an equation in a system?

Back

It means that the point is not a solution to the system.