Solving Systems by Graphing

Front

What is the solution to a system of equations when two lines intersect?

Back

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

Front

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

Back

It means the lines are parallel and never intersect.

Front

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

Back

It means the lines are coincident, or the same line, and overlap completely.

Front

How can you determine if two lines are parallel from their equations?

Back

If the lines have the same slope but different y-intercepts, they are parallel.

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

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b).

Front

If two lines have slopes of 2 and -1, what can you say about their intersection?

Back

The lines will intersect at one point since they have different slopes.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the graphs of the equations on a coordinate plane.

Front

How can you check if your solution to a system of equations is correct?

Back

Substitute the solution back into the original equations to see if both equations are satisfied.