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

They have no solutions because they never intersect.

Front

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

Back

The point where the two lines intersect.

Front

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

Back

There are infinitely many solutions because every point on the line is a solution.

Front

How can 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 of a line?

Back

The rate at which the line rises or falls, calculated as the change in y over the change in x.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis.

Front

If a system of equations has one solution, what does this indicate about the lines?

Back

The lines intersect at exactly one point.

Front

What is the solution to the system of equations y = 2x + 1 and y = 2x - 3?

Back

No solution, as the lines are parallel.

Front

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

Back

(1, 3), the point where the lines intersect.