Systems Elimination (Easy)

Front

What is a solution to a system of equations?

Back

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

Front

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

Back

To check if a point is a solution, 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 a point is a solution to a system of equations?

Back

It means that the point lies on the graph of both equations, representing the intersection of the two lines.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines represented by the equations.

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

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

Back

If two lines are parallel, it means they have no intersection points, and thus, the system has no solution.

Front

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

Back

If two lines coincide, they lie on top of each other, meaning there are infinitely many solutions to the system.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is a consistent system of equations?

Back

A consistent system has at least one solution, which can be either a single point or infinitely many points.

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solutions, meaning the equations represent parallel lines.