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 verify if a point is a solution to a system of equations?

Back

You can verify if a point is a solution by substituting the x and y coordinates into each equation and checking if both equations are true.

Front

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

Back

If two equations intersect at a point, that point is the solution to the system, meaning it satisfies both equations.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations is the intersection of the lines represented by each equation on a coordinate plane.

Front

What is the significance of the ordered pair (1, -2) in a system of equations?

Back

The ordered pair (1, -2) is the solution to the system of equations, meaning it satisfies both equations.

Front

What does it indicate if a point does not satisfy one of the equations in a system?

Back

If a point does not satisfy one of the equations, it is not a solution to the system.

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.

Front

What is the difference between a consistent and inconsistent system of equations?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

Front

What is a dependent system of equations?

Back

A dependent system has infinitely many solutions, as the equations represent the same line.

Front

How do you determine if a system of equations has a unique solution?

Back

A system has a unique solution if the lines represented by the equations intersect at exactly one point.