Essentials Graphing Systems of Equations

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, representing the values of the variables that satisfy both equations.

Front

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

Back

It means that the lines intersect at exactly one point.

Front

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

Back

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

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines: if slopes are equal and y-intercepts are different, no solution; if slopes are equal and y-intercepts are the same, infinitely many solutions; if slopes are different, one solution.

Front

What is the slope of a line?

Back

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

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) in the equation y = mx + b.

Front

What is the standard form of a linear equation?

Back

The standard form is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you graph a linear equation?

Back

To graph a linear equation, find the y-intercept, plot it on the graph, use the slope to find another point, and draw a line through the points.

Front

What is the difference between intersecting lines and parallel lines?

Back

Intersecting lines cross at one point, while parallel lines never meet and have the same slope.