Solving Linear Systems by Graphing

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 a system of equations has no solution?

Back

It means that the lines are parallel and will never intersect.

Front

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

Back

It means that the two lines are the same line, overlapping each other.

Front

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

Back

If the slopes of the two lines are equal, the lines 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

What does it mean if two lines intersect at one point?

Back

It means that the system of equations has exactly one solution.

Front

How can you graph a linear equation?

Back

You can graph a linear equation by plotting the y-intercept and using the slope to find another point.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of the lines corresponding to each equation plotted on the same coordinate plane.