Graphing Systems of Equations

Front

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

Back

The two lines intersect at a single point.

Front

What is the graphical representation of the equations y = x and y = -x?

Back

The lines intersect at the origin (0, 0).

Front

How do you solve a system of equations by graphing?

Back

Graph both equations on the same coordinate plane and identify the point(s) where they intersect.

Front

What is the solution to the system of equations y = 6x - 4 and y = -x + 3?

Back

The solution is the point (1, 2).

Front

What does it mean if a system of linear equations has no solution?

Back

The lines are parallel and never intersect.

Front

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

Back

The system has no solution because the lines are parallel.

Front

What is the significance of the point of intersection in a system of equations?

Back

It represents the solution to the system, where both equations are satisfied.

Front

How can you determine if a system of equations has infinitely many solutions?

Back

If the two equations represent the same line, they have infinitely many solutions.

Front

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

Back

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

Front

What does the slope of a line represent in a graph?

Back

The slope represents the rate of change of y with respect to x.