Systems of Equations Check-in

Front

What are parallel lines?

Back

Parallel lines are lines in a plane that never intersect. They have the same slope but different y-intercepts.

Front

What does it mean when two lines have the same slope?

Back

When two lines have the same slope, they are parallel and will never intersect.

Front

What is the solution to a system of equations?

Back

The solution to a system of equations is the point where the two lines intersect, representing the values of the variables that satisfy both equations.

Front

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

Back

A system of equations has no solution if the lines are parallel and never intersect.

Front

What does it mean if a system of equations has infinite solutions?

Back

A system of equations has infinite solutions if the two equations represent the same line, meaning they intersect at every point on that line.

Front

How do you determine the solution of a system of equations graphically?

Back

To determine the solution graphically, plot both equations on the same graph and identify the point where they intersect.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x is zero.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise over run).

Front

If two lines intersect at a point, what does that indicate about the system of equations?

Back

If two lines intersect at a point, it indicates that the system of equations has a unique solution.

Front

What is the graphical representation of a system of equations with infinite solutions?

Back

The graphical representation of a system with infinite solutions is a single line, as both equations describe the same line.