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 two lines are parallel in a system of equations?

Back

It means there is no solution to the system because the lines never intersect.

Front

What does it mean if two lines are the same in a system of equations?

Back

It means there are infinitely many solutions because every point on the line is a solution.

Front

What is the graphical representation of a solution to a system of equations?

Back

The point where the two lines intersect.

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines.

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 do you solve a system of equations by graphing?

Back

Graph both equations on the same coordinate plane and identify the intersection point.

Front

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

Back

(1, 3)

Front

What does it mean if a system of equations has one solution?

Back

The lines intersect at exactly one point.

Front

What is the solution to the system: y = 1/2x + 2 and y = -3x + 9?

Back

(2, 3)