Basic Systems of Equations

Front

What is a system of equations?

Back

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

Front

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

Back

They have the same slope and different y-intercepts, meaning they never intersect and have no solutions.

Front

What is the solution of a system of equations?

Back

The point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations in the system.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The equations represent the same line, having the same slope and y-intercept.

Front

How can you determine if a system of equations has no solution?

Back

If the lines are parallel, they will never intersect, indicating no solution.

Front

What is the graphical representation of a system of equations?

Back

The graphs of the equations plotted on a coordinate plane.

Front

What is the significance of the slope in a system of equations?

Back

The slope indicates the steepness of the line and helps determine if lines are parallel or intersecting.

Front

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

Back

The system has exactly one solution, which is the coordinates of the intersection point.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.

Front

What is an inconsistent system of equations?

Back

A system that has no solutions.