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

It means the system has no solutions because the lines never intersect.

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the equations.

Front

What is the solution of a system of equations?

Back

The point where the graphs of the equations intersect.

Front

What does it mean if two equations represent the same line?

Back

The system has infinitely many solutions.

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope is 3.

Front

If a system of equations has one solution, what does that indicate about the lines?

Back

The lines intersect at exactly one point.

Front

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

Back

The point of intersection of the lines on a graph.

Front

What happens to the solutions if the slopes of two lines are equal but the y-intercepts are different?

Back

The system has no solutions.

Front

How can you express a system of equations in standard form?

Back

By writing the equations in the form Ax + By = C.