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 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, which is the solution.

Front

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

Back

The lines coincide, meaning they are the same line.

Front

How do you graph the equation y = mx + b?

Back

Plot the y-intercept (b) on the y-axis, then use the slope (m) to find another point.

Front

What is the slope of the line represented by the equation y = 1/2x + 2?

Back

The slope is 1/2.

Front

What is the y-intercept of the equation y = -3x + 9?

Back

The y-intercept is 9.

Front

How can you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.

Front

How can you determine if two lines are perpendicular?

Back

If the product of their slopes is -1.

Front

What is the solution to the system of equations y = 2x + 1 and y = 4x - 1?

Back

(1, 3) is the solution.