Systems of Graphing

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 a system of equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has one solution?

Back

The lines intersect at exactly one point.

Front

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

Back

The lines overlap each other, representing the same line.

Front

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

Back

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

Front

What is the graphical representation of a system of equations?

Back

It is represented by the intersection points of the lines on a graph.

Front

What is the solution to the system of equations y = 2x + 1 and y = 2x - 3?

Back

No solution, the lines are parallel.

Front

What is the solution to the system of equations y = x + 2 and y = -x + 4?

Back

(1, 3), the lines intersect at this point.

Front

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

Back

3, which indicates the line rises 3 units for every 1 unit it moves to the right.

Front

What is the y-intercept of the equation y = -2x + 5?

Back

5, the point where the line crosses the y-axis.