Ordered Pair Solutions to Systems of Equations

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers used to represent a point in a coordinate system, written in the form (x, y).

Front

How do you determine if an ordered pair is a solution to a system of equations?

Back

An ordered pair is a solution if it satisfies both equations in the system, meaning when you substitute x and y into both equations, they hold true.

Front

What does it mean for an equation to be true?

Back

An equation is true when both sides of the equation are equal after substituting the values of the variables.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables that are solved together.

Front

What is the graphical representation of a solution to a system of equations?

Back

The solution is represented by the point where the graphs of the equations intersect.

Front

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

Back

The intersection point represents the values of the variables that satisfy all equations in the system.

Front

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

Back

Substitute the x and y values of the point into each equation. If both equations are satisfied, the point is a solution.

Front

What does it mean if two lines in a system of equations are parallel?

Back

If two lines are parallel, they have no points of intersection, meaning there is no solution to the system.

Front

What does it mean if two lines in a system of equations coincide?

Back

If two lines coincide, they are the same line, meaning there are infinitely many solutions 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.