Solve Systems 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 to have no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean for a system to have one solution?

Back

The lines intersect at exactly one point, which is the solution to the system.

Front

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

Back

The lines representing the equations are the same line, meaning they overlap completely.

Front

How do you graph a linear equation?

Back

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

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the y-intercept of the equation y = 2x - 11?

Back

The y-intercept is -11.

Front

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

Back

The slope is 2.

Front

How do you determine the solution of a system of equations graphically?

Back

The solution is the point where the two lines intersect.

Front

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

Back

(1, 3)