Graphing 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 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 no solution?

Back

The lines are parallel and never intersect.

Front

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

Back

The lines are the same, meaning they overlap completely.

Front

How do you find the solution to a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) of intersection.

Front

What is the graphical representation of the equation y = 2x + 1?

Back

A straight line with a slope of 2 and a y-intercept of 1.

Front

What is the slope of the line represented by the equation y = -3x + 4?

Back

The slope is -3.

Front

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

Back

The y-intercept is -2.

Front

If two lines have the same slope but different y-intercepts, what can be said about the system of equations?

Back

The system has no solution.

Front

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

Back

The solution is (1, 3).