Solving Systems by Graphing

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

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

Back

It means to graph the equations on the same coordinate plane and find the point(s) where they intersect.

Front

What is the solution to a system of equations?

Back

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

Front

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

Back

It means there is no solution to the system, as the lines never intersect.

Front

What does it mean if two lines coincide when graphing a system of equations?

Back

It means there are infinitely many solutions, as the lines overlap completely.

Front

How do you determine the solution from a graph?

Back

Identify the coordinates of the intersection point of the graphed lines.

Front

What is the importance of the y-intercept in graphing linear equations?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x=0.

Front

What is the slope of a line?

Back

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

Front

How can you tell if a system of equations has no solution by looking at the graph?

Back

If the lines are parallel and do not intersect, the system has no solution.

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.