Solving Systems of Equations by Graphing

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean to solve a system of equations by graphing?

Back

It means to find the point(s) where the graphs of the equations intersect, which represents the solution(s) to the system.

Front

What is the solution to a system of equations?

Back

The point(s) where the equations intersect on a graph, representing the values of the variables that satisfy all equations.

Front

What does it indicate if two lines are parallel when graphing a system of equations?

Back

It indicates that the system has no solution, as the lines never intersect.

Front

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

Back

It means that the equations represent the same line, and every point on that line is a solution.

Front

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

Back

By plotting the equations on a graph and identifying the intersection point(s).

Front

What is the graphical representation of the equation y = 2x + 1?

Back

A straight line with a slope of 2 and a y-intercept of 1.

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 between two points on the line.

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 does it mean if two lines intersect at a single point?

Back

It means that the system of equations has a unique solution, represented by the coordinates of the intersection point.