Solving Systems of Equations by 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 for a system of equations to have one solution?

Back

The graphs of the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

The graphs of the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

The graphs of the equations lie on top of each other, representing the same line.

Front

How do you graph a linear equation?

Back

Identify the y-intercept and use the slope to find another point.

Front

What is the y-intercept of a linear equation?

Back

The point where the line crosses the y-axis (x=0).

Front

What is the slope of a line?

Back

The ratio of the rise (change in y) to the run (change in x).

Front

How can you determine if two lines are parallel?

Back

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

Front

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

Back

(1, 3) - The point where the two lines intersect.

Front

What is the graphical representation of the equation y = 3?

Back

A horizontal line that crosses the y-axis at 3.