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 are the same line, meaning they intersect at every point on the line.

Front

How do you solve a system of equations by graphing?

Back

Graph each equation on the same coordinate plane and identify the point(s) of intersection.

Front

What is the graphical representation of the equation 2x + 3y = 6?

Back

A straight line that intersects the x-axis at (3,0) and the y-axis at (0,2).

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

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: 3x + 2y = 16 and 7x + y = 19?

Back

(2, 5)

Front

What does the graph of the equations 2x + y = 4 and 2x + y = 6 look like?

Back

Two parallel lines with no points of intersection.