5.2 Graphing Systems

Front

What is the solution to the system of equations represented by the intersection of two lines?

Back

The solution is the point where the two lines intersect, represented as an ordered pair (x, y).

Front

What does it mean if two lines are parallel?

Back

Parallel lines never intersect because they have the same slope.

Front

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

Back

It indicates that the two lines are intersecting lines.

Front

How can you determine the solution to a system of equations graphically?

Back

By graphing the equations and identifying the point of intersection.

Front

What is the significance of the slopes of two lines in a system of equations?

Back

If the slopes are equal, the lines are parallel; if they are different, the lines will intersect.

Front

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

Back

It means the lines are parallel and will never intersect.

Front

What is an ordered pair in the context of graphing equations?

Back

An ordered pair (x, y) represents a specific point on the graph where x is the horizontal coordinate and y is the vertical coordinate.

Front

How do you find the y-intercept of a linear equation?

Back

Set x = 0 in the equation and solve for y.

Front

What is the y-intercept of the equation y = 2x + 3?

Back

The y-intercept is 3, which is the point (0, 3) on the graph.

Front

What does it mean if two lines are the same line?

Back

It means the system of equations has infinitely many solutions.