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

How can you tell if a point is a solution to a system?

Back

The (x,y) coordinates satisfy both equations.

Front

What does it mean if two lines intersect on a graph?

Back

The intersection point is the solution to the system of equations.

Front

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

Back

(1, 3)

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 infinite solutions?

Back

The equations represent the same line.

Front

How do you graph a linear equation?

Back

Find two or more points that satisfy the equation and connect them with a straight line.

Front

What is the slope of a line?

Back

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

Front

What is the y-intercept of a line?

Back

The y-coordinate where the line crosses the y-axis.

Front

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

Back

By plotting both equations on the same graph and identifying their intersection point.